相关论文: Random walk of second class particles in product s…
In the case of a rarefaction fan in a non-stationary Hammersley process, we explicitly calculate the asymptotic behavior of the process as we move out along a ray, and the asymptotic distribution of the angle within the rarefaction fan of a…
We consider a system of $N$ particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…
Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…
We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…
We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively…
In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest neighbor interactions. We consider two kinds of inter-particle interactions. In one case, the particle-hole symmetry…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
We investigate properties of non-translation-invariant measures, describing particle systems on $\bbz$, which are asymptotic to different translation invariant measures on the left and on the right. Often the structure of the transition…
Double (or parity conserving) branching annihilating random walk, introduced by Sudbury in '90, is a one-dimensional non-attractive particle system in which positive and negative particles perform nearest neighbor hopping, produce two…
We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…