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 model, we show that the classical Einstein relation does not hold.
We study the stationary state of driven-dissipative activated random walk on an interval of length $n$ and prove that subintervals down to size $\log n$ have particle density near the critical value. We then deduce that the avalanche area is heavy-tailed and that the process forgets an initial stationary state after $o...
Tobias Johnson, Matthew Junge, Josh Meisel· 0 citations
We study a random walk in $\mathbb{Z}^d$ in a dynamical random environment constituted of independent null recurrent birth-and-death chains, and establish a scaling limit result for the position of the walker in terms of a sublinear time change of Brownian motion, thus establishing subdiffusivity, in contrast to a diff...
In this paper we consider random walks moving in a dynamic random environment that is completely resampled with probability $p$ after each step of the random walker. This resampling yields a straightforward regeneration structure and limit theorems, such as a law of large numbers with a limiting speed $v(p)$ that depen...
We propose a new variant of a biased random walk on a Galton-Watson tree, in which some vertices have infinitely many children. These vertices induce a natural regeneration structure, which allows to study differentiability and also monotonicity of the speed of the random walk in the bias parameter. Additionally, we sh...
We consider the maximum Mt of branching random walk in a space-inhomogeneous random environment on Z. In this model the branching rate while at some location x∈Z is randomized in an i.i.d. manner. We prove that there is a centering m˜t depending only on the environment such that (Mt−m˜t)t≥0 is tight in an annealed sens...
Xaver Kriechbaum· The Annals of Applied Probab...· 0 citations
For simple random walk on infinite clusters of Bernoulli bond percolation on Cayley graphs of hyperbolic groups, we prove that the drift and asymptotic entropy depend continuously on the percolation parameter throughout the supercritical phase. Together with the dimension formula, this implies continuity of the Hausdor...
K. Sakamoto· 0 citations
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