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We study a biased random walk on the interlacement set of $mathbb{Z}^d$ for $dgeq 3$. Although the walk is always transient, we can show, in the case $d=3$, that for any value of the bias the walk has a zero limiting speed and actually moves slower than any power.
We consider a simple random walk on $mathbb{Z}^d$ started at the origin and stopped on its first exit time from $(-L,L)^d cap mathbb{Z}^d$. Write $L$ in the form $L = m N$ with $m = m(N)$ and $N$ an integer going to infinity in such a way that $L^2 s
We study the asymptotic behaviour of once-reinforced biased random walk (ORbRW) on Galton-Watson trees. Here the underlying (unreinforced) random walk has a bias towards or away from the root. We prove that in the setting of multiplicative once-reinf
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition kernels w
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Su
Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected lifetime.