Related papers: Localization for Branching Random Walks in Random …
We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In…
We consider random walks in a random environment of the type p_0+\gamma\xi_z, where p_0 denotes the transition probabilities of a stationary random walk on \BbbZ^d, to nearest neighbors, and \xi_z is an i.i.d. random perturbation. We give…
We study biological evolution on a random fitness landscape where correlations are introduced through a linear fitness gradient of strength $c$. When selection is strong and mutations rare the dynamics is a directed uphill walk that…
This paper concerns a random walk that moves on the integer lattice and has zero mean and a finite variance. We obtain first an asymptotic estimate of the transition probability of the walk absorbed at the origin, and then, using the…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
We analyze the properties of population spreading in environments with spatial anisotropy within the frames of a lattice model of asymmetric (biased) random walkers. The expressions for the universal shape characteristics of the…
We study the critical centered branching random walk with offspring and displacement distributions having finite variance, under minimal assumptions on its structure. We show that the probability that the position of the right-most particle…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
We introduce range-controlled random walks with hopping rates depending on the range $\mathcal{N}$, that is, the total number of previously distinct visited sites. We analyze a one-parameter class of models with a hopping rate…
We consider a random walk in an i.i.d. random environment on Zd and study properties of its large deviation rate function at the origin. It was proved by Comets, Gantert and Zeitouni in dimension d = 1 in 1999 and later by Varadhan in…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
In this article, we study the maximal displacement of critical branching random walk in random environment. Let $M_n$ be the maximal displacement of a particle in generation $n$, and $Z_n$ be the total population in generation $n$, $M$ be…
We prove a quenched invariance principle for a class of random walks in random environment on $\mathbb{Z}^d$, where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the…
We analyze a variant of the Noisy $K$-Branching Random Walk, a population model that evolves according to the following procedure. At each time step, each individual produces a large number of offspring that inherit the fitness of their…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
Consider a critical branching random walk on $\mathbb{Z}^d$, $d\geq 1$, started with a single particle at the origin, and let $L(x)$ be the total number of particles that ever visit a vertex $x$. We study the tail of $L(x)$ under suitable…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We consider a supercritical symmetric continuous-time branching random walk on a multidimensional lattice with a finite number of particle generation sources of varying positive intensities without any restrictions on the variance of jumps…