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May 2021 Limit law for the cover time of a random walk on a binary tree
Amir Dembo, Jay Rosen, Ofer Zeitouni
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Ann. Inst. H. Poincaré Probab. Statist. 57(2): 830-855 (May 2021). DOI: 10.1214/20-AIHP1098

Abstract

Let Tn denote the binary tree of depth n augmented by an extra edge connected to its root. Let Cn denote the cover time of Tn by simple random walk. We prove that the sequence of random variables Cn2(n+1)mn, where mn is an explicit constant, converges in distribution as n, and identify the limit.

Soit Tn l’arbre binaire de profondeur n, augmenté par une arête attachée à la racine. Soit Cn le temps de recouvrement de Tn par une marche aléatoire simple. Nous montrons que la suite de variables aléatoires Cn2(n+1)mn, avec mn une constante explicite, converge quand n. Nous identifions la limite.

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Amir Dembo. Jay Rosen. Ofer Zeitouni. "Limit law for the cover time of a random walk on a binary tree." Ann. Inst. H. Poincaré Probab. Statist. 57 (2) 830 - 855, May 2021. https://doi.org/10.1214/20-AIHP1098

Information

Received: 18 August 2019; Revised: 4 May 2020; Accepted: 25 August 2020; Published: May 2021
First available in Project Euclid: 13 May 2021

Digital Object Identifier: 10.1214/20-AIHP1098

Subjects:
Primary: 60G50, 60J80, 60J85

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

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Vol.57 • No. 2 • May 2021
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