# Chiranjib Mukherjee -- "Compactness, large deviations and the polaron"

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*schedule*
le mardi 16 janvier 2018 de 16h30 à 17h30

**Organisé par :**LPSM

**Intervenant :**Chiranjib Mukherjee (Münster)

**Lieu :**Salle Paul Lévy (113) 1er étage Tours 16-26, Jussieu.

**Sujet :**"Compactness, large deviations and the polaron"

**Résumé :**

In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities. In such estimates, upper bounds for such small probabilities often require compactness of the ambient space, which is often absent in problems arising in statistical mechanics (for example, distributions of local times of Brownian motion in the full space Rd). Motivated by such a problem, we present a robust theory of “translation-invariant compactification” of probability measures in Rd. Thanks to an inherent shift-invariance of the underlying problem, we are able to apply this abstract theory painlessly and solve a long standing problem in statistical mechanics, the polaron problem as well as its mean-field counterpart.

This talk is based on results obtained in collaboration with S. R. S. Varadhan (New York), as well as with Erwin Bolthausen (Zurich) and Wolfgang Koenig (Berlin).