We consider a branching random walk on \(\Z^d\) in a random environment given by Bernoulli site percolation with parameter \(p\in (0,1)\). In this model, each particle located at an open site reproduces according to a law \(\mu_\circ\), whereas a particle at a closed site reproduces according to another law \(\mu_\bullet\). Each newly born child performs an independent simple random walk jump from the position of its parent. We study the quenched survival probability under various assumptions on \((\mu_\circ, \mu_\bullet)\) and establish a Yaglom theorem when both offspring distributions are critical.
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 study continuous-time supercritical branching random walks in space-inhomogeneous random environment on the Hamming cube $\{0,1,\dots,b-1\}^d$, where the reproduction laws at each site are i.i.d. sampled. This serves as an idealized model for RNA sequence evolution with mutation--selection balance. The reproduction...
We study the limit shape of the range of the random walk excited to the center on $\mathbb Z^d$, with $d\geq2$. A cookie is placed at each nonzero vertex. On its first visit to such a vertex, the walker consumes the cookie and takes its next nearest-neighbor step with a bias toward the origin. On a visit to the origin,...
We consider a competition between two independent random walks on a cycle of length $N$. Each vertex is claimed by the walker that visits it first, and remains claimed thereafter. We prove that if the initial distance between the walkers is $d$, then the expected number of edges whose endpoints are claimed by different...
S. Chatterjee, Nadya Nabahi, Grigory Terlov· 1 citation
We consider a branching random walk on $\mathbb{Z}^2$ with critical offspring of mean $1$ and spatial motion governed by the jumps of a lazy simple random walk. For every site $x\in\mathbb{Z}^2$, we obtain a uniform asymptotical estimate for the local survival probability, i.e., the probability that there are particles...
We consider a once-excited random walk on $\mathbb{Z}^d$, $d \ge 2$, where the walk on its first visit has a bias of constant strength $\beta>0$ toward the origin and moves like a simple symmetric random walk on subsequent visits to that site. We show that the walk is recurrent and prove an almost sure spherical shape...
Arvind Singh· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
