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Branch of probability theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While
Large_deviations_theory
Theorem
mathematics — specifically, in large deviations theory — the contraction principle is a theorem that states how a large deviation principle on one space "pushes
Contraction principle (large deviations theory)
Contraction_principle_(large_deviations_theory)
Fundamental result in the theory of large deviations
Cramér's theorem is a fundamental result in the theory of large deviations, a subdiscipline of probability theory. It determines the rate function of a series
Cramér's theorem (large deviations)
Cramér's_theorem_(large_deviations)
Theorem in mathematics
In mathematics, Laplace's principle is a basic theorem in large deviations theory which is similar to Varadhan's lemma. It gives an asymptotic expression
Laplace principle (large deviations theory)
Laplace_principle_(large_deviations_theory)
Probability function
large deviations theory, a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large deviation
Rate_function
Theorem in the large deviations theory of stochastic processes
to Mark Freidlin and Alexander D. Wentzell) is a result in the large deviations theory of stochastic processes. Roughly speaking, the Freidlin–Wentzell
Freidlin–Wentzell_theorem
Concept in stochastic analysis
the Contraction principle in large deviations theory reduces Freidlin–Wentzell's problem to demonstrating the large deviation principle for ( t , ε B t )
Rough_path
Mathematical formula
specifically, in large deviations theory — the tilted large deviation principle is a result that allows one to generate a new large deviation principle from
Tilted large deviation principle
Tilted_large_deviation_principle
In mathematics, Varadhan's lemma is a result from the large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the
Varadhan's_lemma
Russian-American probability theorist
Freidlin–Wentzell theory, which is an important part of the large deviations theory. Freidlin and Wentzell are the authors of the first monograph on the large deviations
Mark_Freidlin
^{n}} to functional Wiener integration. The theorem is used in the large deviations theory of stochastic processes. Roughly speaking, out of Schilder's theorem
Schilder's_theorem
Generalization of the binomial distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts
Multinomial_distribution
Study of convergence properties of statistical estimators
In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework
Asymptotic theory (statistics)
Asymptotic_theory_(statistics)
Mathematical theorem
distribution. In the language of large deviations theory, Sanov's theorem identifies the rate function for large deviations of the empirical measure of a
Sanov's_theorem
divergence Le Cam's theorem Large deviations theory Contraction principle (large deviations theory) Varadhan's lemma Tilted large deviation principle Rate function
List_of_probability_topics
Russian mathematician (1931–2026)
theory, mathematical statistics, stochastic processes, queueing theory, large deviations, random walks, and asymptotic methods. He authored several influential
Aleksandr_Borovkov
Mathematical concept
{\displaystyle a} and b . {\displaystyle b.} This estimate is useful in large deviations theory under exponential moment conditions, because b ln b {\displaystyle
Young's inequality for products
Young's_inequality_for_products
Topic in mathematics
number of samples. Such results are studied in large deviations theory; intuitively, it is the large deviations that would violate equipartition, but these
Asymptotic equipartition property
Asymptotic_equipartition_property
Representation of a type of random process
has been suppressed by assuming that the variable has been measured as deviations from its mean) as X t = 1 φ ( B ) ε t . {\displaystyle X_{t}={\frac {1}{\varphi
Autoregressive_model
tests are computed using Sanov's theorem and other results from large deviations theory. There are various methods used to show that an error exponent
Error exponents in hypothesis testing
Error_exponents_in_hypothesis_testing
L-theory the K-theory of quadratic forms. Large deviations theory part of probability theory studying events of small probability (tail events). Large sample
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Measure of variation in statistics
variance being the average of the squared deviations from the mean). A useful property of the standard deviation is that, unlike the variance, it is expressed
Standard_deviation
Notion for convergence of metric spaces
the concept of Gromov–Hausdorff limits is closely related to large-deviations theory. Intrinsic flat distance David A. Edwards, "The Structure of Superspace"
Gromov–Hausdorff_convergence
Method for approximate evaluation of integrals
descent Saddlepoint approximation method Large deviations theory Laplace principle (large deviations theory) Laplace's approximation Tierney, Luke; Kadane
Laplace's_method
Mathematical result in large deviations theory
is a result in large deviations theory. Heuristically speaking, the Dawson–Gärtner theorem allows one to transport a large deviation principle on a “smaller”
Dawson–Gärtner_theorem
Branch of statistics focusing on large deviations
Fisher–Tippett–Gnedenko theorem Generalized extreme value distribution Large deviation theory Outlier Pareto distribution Pickands–Balkema–de Haan theorem Rare
Extreme_value_theory
Mathematics of convex functions and sets
probability measures by testing them against convex functions, and large deviations theory uses the Legendre–Fenchel transform to express rate functions as
Convex_analysis
Stochastic volatility model used in derivatives markets
implement in computer code, and lends itself well to risk management of large portfolios of options in real time. It is convenient to express the solution
SABR_volatility_model
standard deviations. This is a large deviation. Though rare in a small domain (of space or/and time), large deviations may be quite usual in a large domain
Large deviations of Gaussian random functions
Large_deviations_of_Gaussian_random_functions
Topics referred to by the same term
a German xDT format to transfer laboratory tests Large deviations theory, field of probability theory Learning Design and Technology, an academic program
LDT
Mathematical transformation
for instance, the same "pull" between a capacitor's plates. In large deviations theory, the rate function is defined as the Legendre transformation of
Legendre_transformation
2009 book on combinatorial enumeration
combinatorial quantities of interest, it also studies limit theorems and large deviations theory for these quantities. Three appendices provide background on combinatorics
Analytic_Combinatorics_(book)
Laplace's rule of succession Laplace smoothing Laplace principle (large deviations theory) Laplace series Laplace transform Two-sided Laplace transform Laplace–Carson
List of things named after Pierre-Simon Laplace
List_of_things_named_after_Pierre-Simon_Laplace
Macroeconomic model
that the deviations in real GNP are comparatively small and might be attributable to measurement errors rather than real deviations. We call large positive
Real_business-cycle_theory
American mathematician
Massachusetts Amherst in 1975. In 1984, he improved a key result in large deviations theory originally due to Jürgen Gärtner, which is now known as Gärtner-Ellis
Richard_S._Ellis
Concept in statistics
way of constructing a GRF is by assuming that the field is the sum of a large number of plane, cylindrical or spherical waves with uniformly distributed
Gaussian_random_field
Equivalence relation on mathematical measures
probability measures are "the same" from the point of view of large deviations theory. Let ( M , d ) {\displaystyle (M,d)} be a metric space and consider
Exponentially equivalent measures
Exponentially_equivalent_measures
Swedish mathematician (1893–1985)
statistics and probabilistic number theory. John Kingman described him as "one of the giants of statistical theory". Harald Cramér was born in Stockholm
Harald_Cramér
Solution to a stochastic differential equation
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion
Diffusion_process
distribution Laplace principle (large deviations theory) LaplacesDemon – software Large deviations theory Large deviations of Gaussian random functions LARS
List_of_statistics_articles
Averages of repeated trials converge to the expected value
In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a large number of independent
Law_of_large_numbers
Indian American mathematician (born 1940)
probability theory and in particular for creating a unified theory of large deviations. He is regarded as one of the fundamental contributors to the theory of
S._R._Srinivasa_Varadhan
Israeli mathematician
filtering theory with applications to control theory (electrical engineering), the spectral theory of random matrices, the theory of large deviations in probability
Ofer_Zeitouni
Welsh mathematical physicist, worked in Ireland
including quantum measurement, Bose–Einstein condensation and large deviations theory. He was a senior professor at the Dublin Institute for Advanced
John_T._Lewis
Statistical measure
Mean absolute error Average absolute deviation Mean signed deviation Mean squared deviation Squared deviations Errors and residuals in statistics Coefficient
Root_mean_square_deviation
On eigenvalues of random matrices
In probability theory, more specifically the study of random matrices, the circular law concerns the distribution of eigenvalues of an n × n {\displaystyle
Circular_law
Israeli computer scientist
information theory. He applied Compression Algorithms based on Approximate String Matching. He presented performance analysis based on large deviations theory (LDT)
Ilan_Sadeh
American mathematician
1955) is an American mathematician, a pioneer in the usage of large deviations theory in performance evaluation and related areas. Weiss received his
Alan_Weiss_(mathematician)
Brazilian mathematical statistician and probability theorist
theorist who is known for her expertise in stochastic processes and large deviations theory. She is a professor of statistics in the Institute of Mathematics
Maria_Eulália_Vares
Concept in measure theory
the concept of exponential tightness, which has applications in large deviations theory. A family of probability measures ( μ δ ) δ > 0 {\displaystyle
Tightness_of_measures
Mathematical approach to quantum physics
expansion parameter) becomes too large, violating the requirement that corrections must be small. Perturbation theory also fails to describe states that
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard
Coefficient_of_variation
Topics referred to by the same term
distributed random variable Cramér's theorem (large deviations), a fundamental result in the theory of large deviations Cramer's theorem (algebraic curves), a
Cramér's_theorem
anl Large deviations theory Contraction principle Cramér's theorem Exponentially equivalent measures Freidlin–Wentzell theorem Laplace principle Large deviations
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Irish educational institution and academic publisher
Lewis had interests including Bose–Einstein condensation and Large deviations theory.[citation needed] The school has three senior professors at present:[when
Dublin Institute for Advanced Studies
Dublin_Institute_for_Advanced_Studies
Topics referred to by the same term
principle may refer to: Contraction principle (large deviations theory), a theorem that states how a large deviation principle on one space "pushes forward"
Contraction_principle
Methods of mathematical approximation
In mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related
Perturbation_theory
Theory of behavioral economics
theory emerged from earlier research by Kahneman and Tversky in the 1970s on heuristics and cognitive biases, which documented systematic deviations from
Prospect_theory
Statistical measure of variability
The absolute deviations about 2 are (1, 1, 0, 0, 2, 4, 7) which in turn have a median value of 1 (because the sorted absolute deviations are (0, 0, 1
Median_absolute_deviation
Bound on probability of a random variable being far from its mean
75% of values must lie within two standard deviations of the mean and 88.88% within three standard deviations for a broad range of different probability
Chebyshev's_inequality
black-body to very high precision; deviations do not exceed 2 parts in 100000. This showed that earlier claims of spectral deviations were incorrect, and essentially
History of the Big Bang theory
History_of_the_Big_Bang_theory
Dutch mathematician (born 1970)
contributed to the book Queues and Lévy fluctuation theory, published in 2015. "Large deviations for Gaussian queues" (2007) Michel Mandjes at the Mathematics
Michel_Mandjes
Mathematical framework for investment risk
the portfolio standard deviation will always be less than the weighted average of the individual assets' standard deviations, thereby creating a "free
Modern_portfolio_theory
Quasiparticle in condensed matter physics
Srinivasa Varadhan, applying large deviation theory to the path integral formulation for the self-energy, showed the large α exactitude of this Landau–Pekar
Polaron
Theory of response to surprise events
that tell you close to nothing. Why? Because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty
Black_swan_theory
Unexpectedly large transient ocean surface wave
early evidence that waves could grow significantly larger than anticipated by conventional theories of wave breaking. This work highlighted that in cases
Rogue_wave
information theory and statistics, Kullback's inequality is a lower bound on the Kullback–Leibler divergence expressed in terms of the large deviations rate
Kullback's_inequality
Procedure to estimate standard deviation from a sample
statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Law of thermodynamics for vapour pressure of a mixture
theoretically possible, as actual examples of mixed deviation exist. The possible physical deviations are not entirely arbitrary however, as they are constrained
Raoult's_law
Pseudoscientific conspiracy theory
Schumann Resonance conspiracy theories are a family of claims that misrepresent the physics of Schumann resonances - natural, extremely low-frequency electromagnetic
Schumann resonances conspiracy theories
Schumann_resonances_conspiracy_theories
Stochastic process in probability theory
In probability theory, an empirical process is a stochastic process that characterizes the deviation of the empirical distribution function from its expectation
Empirical_process
Swiss mathematician (born 1945)
martingale convergence theorems, combinatorial limit theorems, and the large deviations theory. Later in his career he dealt with stochastic models in mathematical
Erwin_Bolthausen
Speculative physics theory
when referring to a specific theory advanced by Ephraim Fischbach in 1971 to explain experimental deviations in the theory of gravity. Later analysis failed
Fifth_force
Mathematical models of strategic interactions
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively
Game_theory
Statistical error measure
squared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-mean square error (RMSE), although some
Mean_absolute_error
Physical theory of the cosmos
one of the underlying principles of the theory of relativity. The cosmological principle states that on large scales the universe is homogeneous and isotropic—appearing
Big_Bang
Theory in evolutionary biology proposed to explain sex ratio deviations in mammals
pressures exist to maintain a 1:1 sex ratio, evolution will favor local deviations from this if one sex has a likely greater reproductive payoff than is
Trivers–Willard_hypothesis
Falsifiable explanation of natural phenomena
A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in
Scientific_theory
Mathematicians of Welsh nationality
Contributed to quantum measurement, Bose–Einstein condensation and large deviations theory. William Morgan 26 May 1750 Bridgend 4 May 1833 London Considered
List_of_Welsh_mathematicians
Description of physical properties at the atomic and subatomic scale
for which quantum mechanics produces only small deviations from classical behavior. These deviations can then be computed based on the classical motion
Quantum_mechanics
American television sitcom (2007–2019)
The Big Bang Theory is an American television sitcom created by Chuck Lorre and Bill Prady for CBS. It aired from September 24, 2007, to May 16, 2019,
The_Big_Bang_Theory
In probability theory and statistics, a continuous-time stochastic process, or a continuous-space-time stochastic process is a stochastic process for which
Continuous-time stochastic process
Continuous-time_stochastic_process
Society, Abel Prize winner. Pioneer of LargeDeviations Theory. C. P. Ramanujam (1938–1974), worked on number theory and algebraic geometry T. S. Vijayaraghavan
List_of_Tamil_people
Israeli-American mathematician
research deals with probability theory and stochastic processes, the theory of large deviations, the spectral theory of random matrices, random walks
Amir_Dembo
Branch of multiobjective optimization
target value to be achieved. Deviations are measured from these goals both above and below the target. Unwanted deviations from this set of target values
Goal_programming
Classical statement of gravity as force
sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities ϕ / c 2 {\displaystyle
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
American mathematician (1940–2025)
Springer. 1979.; reprintings 1997, 2006 An introduction to the theory of large deviations. Springer-Verlag. 1984. with Andrzej Korzeniowski: Korzeniowski
Daniel_W._Stroock
Business process improvement technique
process standard deviation goes up, or the mean of the process moves away from the center of the tolerance, fewer standard deviations will fit between
Six_Sigma
Probability distribution
standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. This
Normal_distribution
Mathematical model for neuron networks
theory Econometrics Ergodic theory Extreme value theory (EVT) Large deviations theory Mathematical finance Mathematical statistics Probability theory
Galves–Löcherbach_model
Statistical measure of how far values spread from their average
In probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their
Variance
French mathematician (born 1969)
Arous & A. Guionnet (1997). "Large deviations for Wigner's law and Voiculescu's non-commutative entropy". Probab. Theory Relat. 108 (4): 517–542. doi:10
Alice_Guionnet
Function in fluid mathematics
indicates the deviation from statically neutral state, with smaller | L | {\displaystyle |L|} values corresponding to larger deviations from neutral conditions
Monin–Obukhov similarity theory
Monin–Obukhov_similarity_theory
Risk of statistically extreme events
three standard deviations may also be broadened, such as the SKEW index which uses the larger tail region starting at two standard deviations. Although tail
Tail_risk
Numbers significantly larger than those used regularly
({n+1})^{k_{n+1}}} is rewritten. For describing numbers approximately, deviations from the decreasing order of values of n are not needed. For example,
Large_numbers
Action or behavior that violates social norms
"deviant" takes on traits that constitute deviance by committing such deviations as conform to the label (so the audience has the power to not label them
Deviance_(sociology)
The Big Bang Theory is an American television sitcom created and executively produced by Chuck Lorre and Bill Prady for CBS. Like the name of the series
List of The Big Bang Theory episodes
List_of_The_Big_Bang_Theory_episodes
Observation far apart from others in statistics and data science
standard deviations from the mean, p is approximately 0.3%, and thus for 1000 trials one can approximate the number of samples whose deviation exceeds
Outlier
Statistics concept
this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the
Errors_and_residuals
Conspiracy theories about the 1983 shootdown
Korean Air Lines Flight 007 alternative theories concerns the various theories put forward regarding the shooting down of Korean Air Lines Flight 007.
Korean Air Lines Flight 007 alternative theories
Korean_Air_Lines_Flight_007_alternative_theories
LARGE DEVIATIONS-THEORY
LARGE DEVIATIONS-THEORY
Female
English
Short form of English Margaret, MARGE means "pearl."
Girl/Female
English
Lark.
Boy/Male
Australian, Welsh
Large Homestead; Large Settlement
Surname or Lastname
English and French
English and French : metonymic occupational name for a boatman, from Middle English, Old French barge ‘boat’, ‘barge’.Dutch : variant of Berg.
Boy/Male
American, Australian, British, Celtic, Christian, English, French, German, Irish, Jamaican, Welsh
Prudent; Large Homestead; Large Settlement
Girl/Female
Persian American
Child of light. Famous Bearer: Margaret Thatcher, former Prime Minister of the United Kingdom.
Surname or Lastname
English and French
English and French : nickname (literal or ironic) meaning ‘generous’, from Middle English, Old French large ‘generous’, ‘free’ (Latin largus ‘abundant’). The English word came to acquire its modern sense only gradually during the Middle Ages; it is used to mean ‘ample in quantity’ in the 13th century, and the sense ‘broad’ first occurs in the 14th. This use is probably too late for the surname to have originated as a nickname for a fat man.
Surname or Lastname
English
English : variant of Sark.German : unexplained.
Boy/Male
Dutch Anglo Saxon
Tall.
Girl/Female
American, Australian
Combination of Latonia and Ray
Girl/Female
Swedish
From the sea.
Boy/Male
French
The red-haired one.
Girl/Female
American, Australian, British, English
Skylark; Lark
Boy/Male
Hindu, Indian
Large
Surname or Lastname
English (mainly Norfolk)
English (mainly Norfolk) : variant of Lark 1.
Girl/Female
British, English
Intelligent
Boy/Male
Tamil
Large quantity
Boy/Male
American, Australian, Chinese, Irish, Welsh
Large Homestead; Great Settlement; Large Village
Boy/Male
British, English
Large
Boy/Male
Dutch
Large.
LARGE DEVIATIONS-THEORY
LARGE DEVIATIONS-THEORY
Biblical
my hope is in her
Boy/Male
Tamil
Gourishankar | கௌரீஷஂகர
Peak of the himalayas, Mt everest
Boy/Male
Latin American Greek
Holy name.
Girl/Female
Hindu, Indian, Traditional
Traditional
Surname or Lastname
English
English : variant of Golder.
Girl/Female
Hindu
Sun, Fire, Goddess Parvati, Graceful or flow of water
Girl/Female
Indian
Happy, Joyful, Cheerful, Glad, Delighted
Girl/Female
American, British, Christian, English, Scandinavian
Affection; Love; Loved One; Famous and Powerful
Boy/Male
Tamil
Lord Shiva
Boy/Male
Hindu
LARGE DEVIATIONS-THEORY
LARGE DEVIATIONS-THEORY
LARGE DEVIATIONS-THEORY
LARGE DEVIATIONS-THEORY
LARGE DEVIATIONS-THEORY
n.
Deviation from ordinary rules; irregularity; deviation from moral rectitude.
adv.
Freely; licentiously.
n.
The voluntary and unnecessary departure of a ship from, or delay in, the regular and usual course of the specific voyage insured, thus releasing the underwriters from their responsibility.
superl.
Unrestrained by decorum; -- said of language.
superl.
Exceeding most other things of like kind in bulk, capacity, quantity, superficial dimensions, or number of constituent units; big; great; capacious; extensive; -- opposed to small; as, a large horse; a large house or room; a large lake or pool; a large jug or spoon; a large vineyard; a large army; a large city.
n.
A large omnibus used for excursions.
superl.
Crossing the line of a ship's course in a favorable direction; -- said of the wind when it is abeam, or between the beam and the quarter.
n.
The state or result of having deviated; a transgression; an act of sin; an error; an offense.
a.
Having a large or generous heart or disposition; noble; liberal.
n.
A large, roomy boat for the conveyance of passengers or goods; as, a ship's barge; a charcoal barge.
a.
Having large hands, Fig.: Taking, or giving, in large quantities; rapacious or bountiful.
n.
A movement or piece in largo time.
n.
A musical note, formerly in use, equal to two longs, four breves, or eight semibreves.
a.
Made large or larger; extended; swollen.
n.
Deviation from moral rectitude.
n.
A large boat used by flag officers.
superl.
Prodigal in expending; lavish.
a.
Deviating.
n.
The act of deviating; a wandering from the way; variation from the common way, from an established rule, etc.; departure, as from the right course or the path of duty.
superl.
Abundant; ample; as, a large supply of provisions.