Related papers: Branching annihilating random walks with parity co…
We consider a non-homogeneous random walks system on $\bbZ$ in which each active particle performs a nearest neighbor random walk and activates all inactive particles it encounters up to a total amount of $L$ jumps. We present necessary and…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Two classes of interacting particle systems on $\mathbb{Z}$ are shown to be Pfaffian point processes at fixed times, and for all deterministic initial conditions. The first comprises coalescing and branching random walks, the second…
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…
One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…
We study the pairwise annihilation process $A+A\to$ inert of a number of random walkers, which originally are localized in a small region in space. The size of the colony and the typical distance between particles increases with time and,…
We study two models with n equivalent absorbing states that generalize the Domany-Kinzel cellular automaton and the contact process. Numerical investigations show that for n=2 both models belong to the same universality class as branching…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…
We study the splitting of regular square lattices subject to stochastic intermittent flows. Various flow patterns are produced by different groupings of the nodes, based on their random alternation between two possible states. The resulting…
The two-dimensional cell-sorting problem is found to be mathematically equivalent to the one-dimensional random walk problem with pair creations and annihilations, i.e. the adhesion probabilities in the cell-sorting model relate…
A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site…
Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.
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…
In this paper, we study a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent of…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population…
A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The…
We study the evolution of an initially random distribution of particles on a square lattice, under certain rules for `growing' and `culling' of particles. In one version we allow the particles to move laterally along the surface (mobile…
A one dimensional non-equilibrium stochastic model is proposed where each site of the lattice is occupied by a particle, which may be of type A or B. The time evolution of the model occurs through three processes: autocatalytic generation…