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Universität Augsburg
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Universität Augsburg
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Professor Dr. Perla Sousi
Cambridge
spricht am
Montag, 28. April 2025
um
15:30 Uhr
im
LMU Room B 349, Theresienstr. 39, 80333 München
über das Thema:
| Abstract: |
| Let X be a simple random walk in $\mathbb{Z}_n^d$ with $d\geq 3$ and let $t_{\rm{cov}}$ be the expected time it takes for X to visit all vertices of the torus. In joint work with Prévost and Rodriguez we study the set $\mathcal{L}_\alpha$ of points that have not been visited by time $\alpha t_{\rm{cov}}$ and prove that it exhibits a phase transition: there exists $\alpha_*$ so that for all $\alpha>\alpha_*$ and all $\epsilon>0$ there exists a coupling between $\mathcal{L}_\alpha$ and two i.i.d. Bernoulli sets $\mathcal{B}^{\pm}$ on the torus with parameters $n^{-(a\pm\epsilon)d}$ with the property that $\mathcal{B}^-\subseteq \mathcal{L}_\alpha\subseteq \mathcal{B}^+$ with probability tending to 1 as $n\to\infty$. When $\alpha\leq \alpha_*$, we prove that there is no such coupling. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Markus Heydenreich |