相关论文: Survival Probability of a Random Walk Among a Pois…
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…
We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random…
In [AJM26], we gave large-time asymptotic bounds on the annealed survival probability of a moving polymer taking values in ${\mathbb R}^d, d \geq 1$. This polymer is a solution of a stochastic heat equation driven by additive spacetime…
There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In…
We consider a random walk among a Poisson cloud of moving traps on ${\mathbb Z}^d$, where the walk is killed at a rate proportional to the number of traps occupying the same position. In dimension $d=1$, we have previously shown that under…
"All misfortune of man comes from the fact that he does not stay peacefully in his room", has once asserted Blaise Pascal. In the present paper we evoke this statement as the "Pascal principle" in regard to the problem of survival of an "A"…
We consider a one-dimensional simple random walk surviving among a field of static soft traps : each time it meets a trap the walk is killed with probability 1--e --$\beta$ , where $\beta$ is a positive and fixed parameter. The positions of…
In this work we study a natural transition mechanism describing the passage from a quenched (almost sure) regime to an annealed (in average) one, for a symmetric simple random walk on random obstacles on sites having an identical and…
We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical…
We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position $x_0$. In particular, we present a remarkably compact derivation of the time-dependent…
We present a systematic analytical approach to the trapping of a random walk by a finite density rho of diffusing traps in arbitrary dimension d. We confirm the phenomenologically predicted e^{-c_d rho t^{d/2}} time decay of the survival…
We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d.\ random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the…
We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length $\ell$ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and…
The dynamics of the survival probability of quantum walkers on a one-dimensional lattice with random distribution of absorbing immobile traps are investigated. The survival probability of quantum walkers is compared with that of classical…
Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. For $d \geq 2$ and $p$ strictly above the critical…
We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments,…
We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary.…
In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These…
We study models of continuous time, symmetric, $\Z^d$-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We…
We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement…