Deviations for the Capacity of the Range of a Random Walk

Amine Asselah (1) , Bruno Schapira (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: Random Walk; Capacity; Range; Large deviations; Moderate deviations

Domaines: Probabilités [math.PR]

Amine Asselah, Bruno Schapira. Deviations for the Capacity of the Range of a Random Walk. 2018. ⟨hal-01832098v1⟩