Session S04 - Random Walks and Related Topics

Thursday, July 15, 13:00 UTC-3

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

Oren Louidor

Technion - Israel's Institute of Technology, Israel   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider a continuous-time random walk on a regular tree of depth $n$ and study its most favorite point among the leaf vertices. We prove that, for the walk started from a leaf vertex and stopped upon hitting the root, under suitable scaling and centering, the maximal time spent at any leaf converges, as $n$ tends to infinity, 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.

Joint work with Marek Biskup (UCLA, United States).

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