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

@inproceedings{Biskup2021ALL, title={A limit law for the most favorite point of simple random walk on a regular tree}, author={Marek Tomasz Biskup and Oren Louidor}, year={2021} }

: 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 square-root local-time…

## One Citation

### Exceptional points of two-dimensional random walks at multiples of the cover time

- MathematicsProbability Theory and Related Fields
- 2022

We study exceptional sets of the local time of the continuous-time simple random walk in scaled-up (by $N$) versions $D_N\subset\mathbb Z^2$ of bounded open domains $D\subset\mathbb R^2$. Upon exit…

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