相关论文: Theory of Branching and Annihilating Random Walks

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…

We revisit the problem of deriving the mean-field values of avalanche critical exponents in systems with absorbing states. These are well-known to coincide with those of an un-biased branching process. Here, we show that for at least 4…

Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…

We consider the probability $P(t)$ that a given site remains unvisited by any of a set of random walkers in $d$ dimensions undergoing the reaction $A+A\to0$ when they meet. We find that asymptotically $P(t)\sim t^{-\theta}$ with a universal…

We present a mean field model for coagulation ($A+A\to A$) and annihilation ($A+A\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is…

The directed bond percolation process is studied in the presence of com- pressible velocity fluctuations with long-range correlations. We discuss a construction of a field theoretic action and a way of obtaining its large scale properties…

Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…

Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…

It will be shown how the directed percolation process in the presence of compressible velocity fluctuations could be formulated within the means of field-theoretic formalism, which is suitable for the renormalization group treatment.

In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it…

We present a functional renormalization group approach for the active to inactive phase transition in directed percolation type systems, in which the transition is approached from the active, finite density phase. By expanding the effective…

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which…

Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly…

We present an exact mapping between two simple spin models: the Fredrickson-Andersen (FA) model and a model of annihilating random walks with spontaneous creation from the vacuum, A+A <-> 0. We discuss the geometric structure of the mapping…

Starting with a percolation model in $\Z^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$.…

Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…

We derive a renormalization method to calculate the spectral dimension $\bar{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of…

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d_c, with…

We introduce a family of classical stochastic processes describing diffusive particles undergoing branching and long-range annihilation in the presence of a parity constraint. The probability for a pair-annihilation event decays as a…