### 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 P_{n} of probability distributions on a space X and asymptotically P_{n} (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 language | English (US) |
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Title of host publication | Proceedings of the International Congress of Mathematicians 2010, ICM 2010 |

Pages | 622-639 |

Number of pages | 18 |

State | Published - Dec 1 2010 |

Event | International Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India Duration: Aug 19 2010 → Aug 27 2010 |

### Publication series

Name | Proceedings of the International Congress of Mathematicians 2010, ICM 2010 |
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### Other

Other | International Congress of Mathematicians 2010, ICM 2010 |
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Country | India |

City | Hyderabad |

Period | 8/19/10 → 8/27/10 |

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### Keywords

- Large deviations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the International Congress of Mathematicians 2010, ICM 2010*(pp. 622-639). (Proceedings of the International Congress of Mathematicians 2010, ICM 2010).