Thursday, December 12, 2024 - 16:15 in V3-201
On the return probability of the simple random walk on Galton-Watson trees
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Peter Müller from LMU München
| Abstract: |
We will review some basics of Galton-Watson trees, introduce random walks on graphs and comment on the relation between heat-kernel bounds and isoperimetric inequalities.
We then focus on the return probability to the root of the simple random walk on supercritical Galton-Watson trees. We explain existing bounds in the literature [Piau, Ann. Probab. 1998] and present a new one which is optimal for Galton-Watson trees with offspring distributions of bounded support. Technically, we build on anchored-expansion techniques introduced by Virag [GAFA 2002] for deterministic graphs with a finite maximal vertex degree. The talk is based on joint work with Jakob Stern.
Within the CRC this talk is associated to the project(s): B10 |
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