Related papers: Branching rate expansion around annihilating rando…

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 develop a criterion for transience for a general model of branching Markov chains. In the case of multi-dimensional branching random walk in random environment (BRWRE) this criterion becomes explicit. In particular, we show that…

We study the simplest irreversible ballistically-controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents…

This paper is devoted to investigating non-equilibrium phase transitions to an absorbing state, which are generically encountered in reaction-diffusion processes. It is a review, based on [Phys. Rev. Lett. 92, 195703; Phys. Rev. Lett. 92,…

We consider a supercritical branching random walk in time-inhomogeneous random environment with a random absorption barrier, i.e.,in each generation, only the individuals born below the barrier can survive and reproduce. Assume that the…

We study branching random walks on Cayley graphs. A first result is that the trace of a transient branching random walk on a Cayley graph is a.s. transient for the simple random walk. In addition, it has a.s. critical percolation…

Let ${Z_{n},n\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at…

Let $T$ be the regular tree in which every vertex has exactly $d\ge 3$ neighbours. Run a branching random walk on $T$, in which at each time step every particle gives birth to a random number of children with mean $d$ and finite variance,…

In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on ${{\mathbb{Z}}^d}$ survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process…

This work extends the studies on the minimum and extremal process of a supercritical branching random walk outside the boundary case which cannot be reduced to the boundary case. We study here the situation where the log-generating function…

Particle hopping is a common feature in heterogeneous media. We explore such motion by using the widely applicable formalism of the continuous time random walk and focus on the statistics of rare events. Numerous experiments have shown that…

We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the…

A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of…

A family of diffusion-annihilation processes is introduced, which is exactly solvable. This family contains parameters that control the diffusion- and annihilation- rates. The solution is based on the Bethe ansatz and using special boundary…

The one-dimensional reaction diffusion process AA->A and A0A->AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in…

In this paper, we study the random walk on a supercritical branching process with an uncountable and unbounded set of types supported on the $d$-regular tree $\mathbb{T}_d$ ($d\geq 3$), namely the cluster $\mathcal{C}_\circ^h$ of the root…

We study the one-dimensional branching random walk in the case when the step size distribution has a stretched exponential tail, and, in particular, no finite exponential moments. The tail of the step size $X$ decays as $\mathbb{P}[X \geq…

We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in $\Z^d$ with $d\ge2$. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to…

Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…