A limit law for the most favorite point of a simple random walk on a regular tree.

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

Date: Dec 07, 2022 at 16:15:00 h
Venue: Sala de Multiusos 1, Primer Piso, Facultad de Matemáticas (Pontificia Universidad Católica de Chile, Santiago)
Speaker: Oren Louidor
Affiliation: Technion, Israel
Coordinator: Avelio Sepúlveda
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Posted on Dec 5, 2022 in Seminario de Probabilidades de Chile, Seminars