Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914233408552960 |
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| author | Erhard, Dirk Poisat, Julien |
| author_facet | Erhard, Dirk Poisat, Julien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00814 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology Erhard, Dirk Poisat, Julien Probability 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. |
| title | Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology |
| topic | Probability |
| url | https://arxiv.org/abs/2304.00814 |