Related papers: Branching Random Walks and their Applications for …
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
The aim of the paper is to describe two models of Covid-19 infection dynamics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily…
Biomolecular networks, such as protein-protein interactions, gene-gene associations, and cell-cell interactions, offer valuable insights into the complex organization of biological systems. These networks are key to understanding cellular…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…
An intrinsic multitype branching structure within the transient (1;R)-RWRE is revealed. The branching structure enables us to specify the density of the absolutely continuous invariant measure for the environments seen from the particle and…
In this paper, we show that a Galton-Watson tree conditioned to have a fixed number of particles in generation $n$ converges in distribution as $n\rightarrow\infty$, and with this tool we study the span and gap statistics of a branching…
We study a branching random walk (BRW) taking its values in a random tree $\bT$ (seen as a family tree) with an infinite line of ancestors that is a variant of a supercritical Galton--Watson (GW) tree with offspring distribution $\nu$. The…
Germ order is a non-standard stochastic order defined through the comparison of the generating functions of the processes. This order was first introduced for branching random walks with a constant breeding law and independent dispersal of…
Consider a branching random walk, where the branching mechanism is governed by a Galton-Watson process, and the migration by a finite range symmetric irreducible random walk on the integer lattice $\mathbb{Z}^d$. Let $Z_n(z)$ be the number…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
Let $\Gamma$ be a non-elementary relatively hyperbolic group with a finite generating set. Consider a finitely supported admissible and symmetric probability measure $\mu$ on $\Gamma$ and a probability measure $\nu$ on $\mathbb{N}$ with…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional…
The food web is a directed graph in which nodes label species and directed links represent the predation between species. The cascade model generates random food webs. The continuum cascade model is a Poisson approximation of the cascade…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…