Large deviations

S. R.S. Varadhan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The theory of Large Deviations deals with techniques for estimating probabilities of rare events. These probabilities are exponentially small in a natural parameter and the task is to determine the exponential constant. To be precise, we will have a family Pn of probability distributions on a space X and asymptotically Pn (A) = exp [-n inf/xεA I(x) + o(n) (equation presented) for a large class of sets, with a suitable choice of the function I(x). This function is almost always related to some form of entropy. There are connections to statistical mechanics as well as applications to the study of scaling limits for large systems. The subject had its origins in the Scandinavian insurance industry where it was used for the evaluation of risk. Since then, it has undergone many developments and we will review some of the recent progress.

Original languageEnglish (US)
Title of host publicationProceedings of the International Congress of Mathematicians 2010, ICM 2010
Pages622-639
Number of pages18
StatePublished - Dec 1 2010
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: Aug 19 2010Aug 27 2010

Publication series

NameProceedings of the International Congress of Mathematicians 2010, ICM 2010

Other

OtherInternational Congress of Mathematicians 2010, ICM 2010
CountryIndia
CityHyderabad
Period8/19/108/27/10

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Keywords

  • Large deviations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Varadhan, S. R. S. (2010). Large deviations. In Proceedings of the International Congress of Mathematicians 2010, ICM 2010 (pp. 622-639). (Proceedings of the International Congress of Mathematicians 2010, ICM 2010).