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Large Deviations for Intersections of Random Walks

Abstract : We prove a Large Deviations Principle for the number of intersections of two independent infinite-time ranges in dimension five and more, improving upon the moment bounds of Khanin, Mazel, Shlosman and Sinaï [KMSS94]. This settles, in the discrete setting, a conjecture of van den Berg, Bolthausen and den Hollander [BBH04], who analyzed this question for the Wiener sausage in finite-time horizon. The proof builds on their result (which was resumed in the discrete setting by Phetpradap [Phet12]), and combines it with a series of tools that were developed in recent works of the authors [AS17, AS19a, AS20]. Moreover, we show that most of the intersection occurs in a single box where both walks realize an occupation density of order one.
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Contributor : Bruno Schapira <>
Submitted on : Tuesday, May 5, 2020 - 6:21:23 PM
Last modification on : Thursday, May 7, 2020 - 1:36:06 AM


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  • HAL Id : hal-02564305, version 1


Amine Asselah, Bruno Schapira. Large Deviations for Intersections of Random Walks. 2020. ⟨hal-02564305⟩



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