相关论文: On multidimensional branching random walks in rand…

Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for…

In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on ${{\mathbb{Z}}^d}$ survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process…

The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase…

In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call…

We consider a continuous-time symmetric branching random walk on the $d$-dimensional lattice, $d\ge 1$, and assume that at the initial moment there is one particle at every lattice point. Moreover, we assume that the underlying random walk…

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance…

We study a random walk on $\mathbb{Z}$ which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, $p$ and $q$. $R$ consecutive right jumps from a site in the $q$-mode are required…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative…

We study the boundary of the range of simple random walk on $\mathbb{Z}^d$ in the transient regime $d\ge 3$. We show that volumes of the range and its boundary differ mainly by a martingale. As a consequence, we obtain a bound on the…

The motivation for this paper is the study of the phase transition for recurrence/transience of a class of self-interacting random walks on trees, which includes the once-reinforced random walk. For this purpose, we define a quantity, that…

Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…

We study a continuous-time branching random walk on the lattice $\mathbb{Z}^{d}$, $d\in \mathbb{N}$, with a single source of branching, that is the lattice point where the birth and death of particles can occur. The random walk is assumed…

In this paper, we study (1,2) and (2,1) random walks in varying environments on the lattice of positive half line. We assume that the transition probabilities at site $n$ are asymptotically constants as $n\rightarrow\infty.$ For (1,2)…

We present a multiscale analysis for the exit measures from large balls in Z^d, d\geq 3, of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding to simple random walk. Our…

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…

The Rademacher random walk associated with a deterministic sequence $(a_n)_{n \geq 1}$ is the walk which starts at zero and, at step $i$, independently steps either up or down by $a_i$ with equal probability. We continue the study begun by…

We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring…

We study how the recurrence and transience of space-time sets for a branching random walk on a graph depends on the offspring distribution. Here, we say that a space-time set $A$ is recurrent if it is visited infinitely often almost surely…

Suppose that the vertices of the Euclidean lattice Z^d are endowed with a random scenery, obtained by tossing a fair coin at each vertex. A random walker, starting from the origin, replaces the coins along its path by i.i.d. biased coins.…