Rodrigo Bazaes, Santiago de Chile: Localization at the boundary for conditioned random walks in random environment in dimension two and higher (Oberseminar Mathematische Stochastik)
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 12.04.2021 von Anita Kollwitz
Geändert am 11.06.2021 von Anita Kollwitz
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