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Deviations for the Capacity of the Range of a Random Walk

Abstract : We obtain estimates for downward deviations for the centered capacity of the range of a random walk on Z d , in dimension d ≥ 5. Our regime of deviations runs from large to moderate. We describe path properties of the random walk under the measure conditioned on downward deviations. The proof is based on a martingale decomposition of the capacity, and a delicate analysis of the corrector term. We also obtain a Large Deviation Principle for upward deviations.
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https://hal.archives-ouvertes.fr/hal-01832098
Contributor : Bruno Schapira <>
Submitted on : Thursday, November 19, 2020 - 12:19:08 PM
Last modification on : Saturday, November 21, 2020 - 3:29:22 AM

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  • HAL Id : hal-01832098, version 3

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Amine Asselah, Bruno Schapira. Deviations for the Capacity of the Range of a Random Walk. 2020. ⟨hal-01832098v3⟩

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