Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology

Dirk Erhard (1) , Julien Poisat (2)

1 UFBA - Universidade Federal da Bahia
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper we introduce a new topology under which the pair empirical measure of a large class of random walks satisfies a strong large deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and Varadhan [12]. This topology is natural for many translation-invariant problems such as the Swiss cheese model [14]. We also adapt our result to certain rescaled random walks. Contents

Domaines: Probabilités [math.PR]

Dirk Erhard, Julien Poisat. Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology. 2023. ⟨hal-04054395v1⟩