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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 the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
We consider the following interacting particle system: There is a ``gas'' of particles, each of which performs a continuous-time simple random walk on $\mathbb{Z}^d$, with jump rate $D_A$. These particles are called $A$-particles and move…
Unlike many particle systems, Activated Random Walk has nontrivial behavior even in one spatial dimension. We prove inner and outer bounds on the spread of n activated random walkers from a single source in Z. The inner bound involves a…
We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show a very strong form of intermittency, where with high probability most of the mass of the system is…
In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
We study a set of Run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation {\theta} of the particle can assume a set of n possible discrete values while in the second case {\theta} is a…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
We introduce a model for diffusion of two classes of particles ($A$ and $B$) with priority: where both species are present in the same site the motion of $A$'s takes precedence over that of $B$'s. This describes realistic situations in…
We consider a two type (red and blue or $R$ and $B$) particle population that evolves on the $d$-dimensional lattice according to some reaction-diffusion process $R+B\to 2R$ and starts with a single red particle and a density $\rho$ of blue…
We study non-interacting Poissonian run-and-tumble particles (RTPs) in two dimensions whose velocity orientations are controlled by an arbitrary circular distribution $Q(\phi)$. RTP-type active transport has been reported to undergo…
We investigate the distribution of occupation times for a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field $U^{{\rm det}}(x)$. When the distribution of energy traps is…
We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a…
We analyze a modification of the Richards growth model by introducing a time-dependent perturbation in the growth rate. This modification becomes effective at a special switching time, which represents the first-crossing-time of the…
We combine particle-based simulations, mean-field rate equations, and Wertheim's theory to study the dynamics of patchy particles in and out of equilibrium, at different temperatures and densities. We consider an initial random distribution…
We consider the Activated Random Walk model in any dimension with any sleep rate and jump distribution and ergodic initial state. We show that the stabilization properties depend only on the average density of particles, regardless of how…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…