## View abstract

### 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. document.getElementById('cloak6249b089e1f17c939359264976269887').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy6249b089e1f17c939359264976269887 = '&#111;r&#101;n.l&#111;&#117;&#105;d&#111;r' + '&#64;'; addy6249b089e1f17c939359264976269887 = addy6249b089e1f17c939359264976269887 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text6249b089e1f17c939359264976269887 = '&#111;r&#101;n.l&#111;&#117;&#105;d&#111;r' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak6249b089e1f17c939359264976269887').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy6249b089e1f17c939359264976269887 + '\'>'+addy_text6249b089e1f17c939359264976269887+'<\/a>';

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).