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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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