Boundary of the Range of Transient Random Walk
Frontière du range d'une marche aléatoire transiente
Résumé
We study the boundary of the range for the simple random walk on Z d in the transient regime d ≥ 3. We show that sizes of the range and its boundary differ mainly by a martingale. As a consequence, we obtain a bound on the variance of order n log n in dimension three. We also establish a central limit theorem in dimension four and larger.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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