Related papers: Random walks in dynamic random environments: A tra…
We examine a class of random walks in random environments on $\mathbb{Z}$ with bounded jumps, a generalization of the classic one-dimensional model. The environments we study have i.i.d. transition probability vectors drawn from Dirichlet…
The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this…
This paper has two main results, which are connected through the fact that the first is a key ingredient in the second. Both are extensions of results concerning directional transience of nearest-neighbor random walks in random environments…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk…
For a Markov chain $Y$ with values in a Polish space, consider the entrance chain, obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit chain, obtained by sampling…
In this article, we consider the speed of the random walks in a (uniformly elliptic and i.i.d.) random environment (RWRE) under perturbation. We obtain the derivative of the speed of the RWRE w.r.t. the perturbation, under the assumption…
A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the…
Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large…
We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a…
We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
We consider a special case of random walk in random environment (RWRE) on Z^d where the environment is periodic (RWPE). Under natural conditions, we show that law of large numbers and central limit theorem holds. In the ballistic nearest…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
We study the asymptotic behavior of the simple random walk on oriented versions of $\mathbb{Z}^2$. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
We consider a model, introduced by Boldrighini, Minlos and Pellegrinotti, of random walks in dynamical random environments on the integer lattice Z^d with d>=1. In this model, the environment changes over time in a Markovian manner,…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…