Large Deviations and Applications

By Francis Comets. International Encyclopedia of Statistical Science, 2011

338 citations recorded by the source corpus.

Subfields: Computational Mechanics, Condensed Matter Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/be59095cf711ee989a991db546052c2a82bacf82

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Citations in the corpus

Distributed Compressive CSIT Estimation and Feedback for FDD Multi-User Massive MIMO Systems (2014, methodology): “We have where ( e 1 ) is from the large deviation theory [44] and (68) can be easily simpliﬁed to be (67).”
Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d (2017, background): “The counterpart of our Theorem 4 in the classical Large Deviation Principle can be found in [2], based on the classical results in [13,87].”
Ergodic Markov processes and Poisson equations (lecture notes) (2016, background): “However, this simple result does not pretend to be even an introduction to large deviations, about which theory see [5, 7, 13, 14, 17, 36, 42], et al.”
Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise (2008, methodology): “The same problem was also treated by Varadhan in [37] and Stroock in [34] by a different approach, which followed the large deviation theory developed by Azencott [2], Donsker-Varadhan [14] and Varadhan [35].”
On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model (2019, methodology): “1 relies on a quantified version of the classical large-deviation approaches as developed for example in [2,26].”
Ruin Probabilities for Risk Processes with Non-Stationary Arrivals and Subexponential Claims (2013, methodology): “See Dembo and Zeitouni (1998) or Varadhan (1984) for general background regarding large deviations and the applications.”
Large deviations of the empirical flow for continuous time Markov chains (2012, methodology): “We recall the definition of the empirical process referring to [19], (IV), [40] for more details.”
Large deviation principle for empirical fields of Log and Riesz gases (2015, background): “er. Quantities obtained by averaging a given conguration over translations as in (1.10), are called \empirical elds". The rst large deviations principles for empirical elds seem to be stated in [Var88], [Fol88] and the relative specic entropy was then formalized by F ollmer and Orey [FO88] in t”
Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “The propetries (i)-(iv) are valid under rather general hypothesis, in particular it is not necessary that the variables {xn} are independent, provided that the correlation function c(k) = 〈(xn+k − 〈x〉)(xn − 〈x〉)〉 goes to zero faster than 1/k as k →∞ [23, 21, 22].”
Representation formula for the entropy and functional inequalities (2010, background): “Let us recall a couple of classical facts about relative entropy, see for instance [23], Section 10, and the references therein.”