Capacity of the range of random walk on Z^d

Amine Asselah (1) , Bruno Schapira (2) , Perla Sousi (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 I2M - Institut de Mathématiques de Marseille
3 DPMMS - Department of Pure Mathematics and Mathematical Statistics

We study the capacity of the range of a transient simple random walk on Z^d. Our main result is a central limit theorem for the capacity of the range for d ≥ 6. We present a few open questions in lower dimensions.

Mots clés: Capacity; Green kernel; Lindeberg-Feller central limit theorem

Domaines: Probabilités [math.PR]

Amine Asselah, Bruno Schapira, Perla Sousi. Capacity of the range of random walk on Z^d. Transactions of the American Mathematical Society, 2018, 370 (11), pp.7627-7645. ⟨10.1090/tran/7247⟩. ⟨hal-01272481⟩