相关论文: Stationary distribution for dioecious branching pa…

This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…

We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…

We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…

We study the high temperature phase of a family of typed branching diffusions initially studied in [Ast\'{e}risque 236 (1996) 133--154] and [Lecture Notes in Math. 1729 (2000) 239--256 Springer, Berlin]. The primary aim is to establish some…

In this paper the distribution of charged particles is constructed under the approximation of ambipolar diffusion. The results of mathematical modelling in two-dimensional case taking into account the velocities of the system are presented.

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…

Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may…

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…

We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…

We consider a two-type reducible branching Brownian motion, defined as a particle system on the real line in which particles of two types move according to independent Brownian motion and create offspring at constant rate. Particles of type…

We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a…

Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…

We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. We analyze the…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…

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 time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…

The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency…

We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…

We study the steady state of a stochastic particle system on a two-dimensional lattice, with particle influx, diffusion and desorption, and the formation of a dimer when particles meet. Surface processes are thermally activated, with…