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### Rodrigo Bazaes, Santiago de Chile: Localization at the boundary for conditioned random walks in random environment in dimension two and higher (Oberseminar Mathematische Stochastik)

##### Wednesday, 23.06.2021 17:00 per ZOOM: 61828242813

We introduce the notion of localization at the boundary for conditioned random walks in i.i.d. and uniformly elliptic random environment on $\mathbb{Z}^d$, in dimensions two and higher. Informally, the walk is localized if its asymptotic trajectory is confined to some region with positive probability. Otherwise, it is delocalized. If $d=2$ or $3$, we prove localization for (almost) all walks. In contrast, for $d\geq 4$, there is a phase transition for environments of the form $\omega_{\varepsilon}(x,e)=\alpha(e)(1+\varepsilon\xi(x,e))$, where $\{\xi(x)\}_{x\in \mathbb{Z}^{d}}$ is an i.i.d. sequence of random variables, and $\varepsilon$ represents the amount of disorder with respect to a simple random walk.

Angelegt am Monday, 12.04.2021 16:55 von kollwit
Geändert am Friday, 11.06.2021 10:19 von kollwit
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