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

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  • Erhard, Dirk
  • Poisat, Julien

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.

Suggested Citation

  • Erhard, Dirk & Poisat, Julien, 2026. "Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology," Stochastic Processes and their Applications, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:spapps:v:194:y:2026:i:c:s0304414925002972
    DOI: 10.1016/j.spa.2025.104853
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