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

Dirk Erhard and Julien Poisat

Stochastic Processes and their Applications, 2026, vol. 194, issue C

Abstract: In this paper we introduce a 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 [1]. This topology is natural for translation-invariant problems such as the downward deviations of the volume of a Wiener sausage or simple random walk, known as the Swiss cheese model [2]. We also adapt our result to some rescaled random walks and provide a contraction principle to the single empirical measure despite a lack of continuity from the projection map, using the notion of diagonal tightness.

Keywords: Large deviation principles; Empirical measure; Occupation measure; Random walk; Compactification (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104853

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