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Pré-Publication, Document De Travail Année : 2024

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

Dirk Erhard
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Résumé

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~\cite{MV2016}. 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~\cite{BBH2001}. 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.
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Dates et versions

hal-04054395 , version 1 (31-03-2023)
hal-04054395 , version 2 (11-04-2024)

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Dirk Erhard, Julien Poisat. Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology. 2024. ⟨hal-04054395v2⟩
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