We consider long-range percolation (LRP) on $\mathbb{Z}^d, d \ge 1$ with connection probabilities $\mathbf{p}(x, y) \approx \frac{\beta}{\|x-y\|^s}$ for $\beta>0$ and $s>\min(2d, d+2)$. Our main result is that the mixing time of the random walk on the giant component of supercritical LRP inside a box of side length $n$...
In this paper we study the constant speed, biased random walk in dynamical random conductances. In certain regimes of the parameters of the model, we prove that the random walk is ballistic. We show annealed and quenched CLT in the full parameter range. Furthermore, as a consequence of the non-reversible nature of this...
We consider collisions of simple random walks on comb graphs $\mathrm{Comb}(\mathbb{Z},H)$, which are obtained by attaching vertical segments of the form $[0,H_x] \cap \mathbb{Z}$ to any point $x$ of the integer axis. For $\mathrm{Comb}(\mathbb{Z},H)$ with profile $H_x(x) = |x| \log^\gamma(|x| \vee 1)$, we show that tw...
Umberto De Ambroggio, Jenson Ng, Maximilian Nitzschner et al.· 0 citations
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