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Article Dans Une Revue Electronic Journal of Probability Année : 2020

Deviations for the Capacity of the Range of a Random Walk

Résumé

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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Dates et versions

hal-01832098 , version 1 (06-07-2018)
hal-01832098 , version 2 (21-09-2018)
hal-01832098 , version 3 (19-11-2020)

Identifiants

  • HAL Id : hal-01832098 , version 3

Citer

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