Related papers: Commuting birth-and-death processes
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…
We study two different types of vector point processes with interacting components, introducing a migration-type effect. The first case concerns two groups which modify their states with rate functions depending on time only. This yields a…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other…
Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic…
We study an immigration effect in the time-changed linear birth-death process where the immigration occurs only if the population goes extinct. We call this process as the time-fractional linear birth-death process with immigration…
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…
We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andr\'a's method (Andra). We give four tables and matrices, and their relations, and…
We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the representations considered correspond to a different set of…
Analytical solutions for time-inhomogeneous linear birth-death processes with immigration are derived. While time-inhomogeneous linear birth-death processes without immigration have been studied by using a generating function approach, the…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
We introduce a model for a population on a lattice with diffusion and birth/death according to 2A->3A and A->0 for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in…
We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some…
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…
In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…
A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements…
We analyze and simulate a two dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two dimensional box, whose boundaries…
Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,...,t_r=1$ we have a discrete Morse function $F_{t_i}:M\to \zr$. In this paper, we study the births and deaths of critical cells for the functions $F_{t_i}$ and present an…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…