March 2024 A limit law for the most favorite point of simplerandom walk on a regular tree
Marek Biskup, Oren Louidor
Author Affiliations +
Ann. Probab. 52(2): 502-544 (March 2024). DOI: 10.1214/23-AOP1644


We consider a continuous-time random walk on a regular tree of finite depth and study its favorite points among the leaf vertices. For the walk started from a leaf vertex and stopped upon hitting the root, we prove that, in the limit as the depth of the tree tends to infinity, the suitably scaled and centered maximal time spent at any leaf converges to a randomly-shifted Gumbel law. The random shift is characterized using a derivative-martingale like object associated with square-root local-time process on the tree.

Funding Statement

This project has been supported in part by the NSF Grant DMS-1954343, ISF Grants No. 1382/17 and 2870/21 and BSF award 2018330.


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Marek Biskup. Oren Louidor. "A limit law for the most favorite point of simplerandom walk on a regular tree." Ann. Probab. 52 (2) 502 - 544, March 2024.


Received: 1 February 2022; Revised: 1 June 2023; Published: March 2024
First available in Project Euclid: 4 March 2024

MathSciNet: MR4718400
Digital Object Identifier: 10.1214/23-AOP1644

Primary: 60G50 , 60G70
Secondary: 05C81

Keywords: extremal value , favorite point , multiplicative chaos , Random walk

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.52 • No. 2 • March 2024
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