Related papers: Branching Random Walks and their Applications for …
We study a generalized branching random walk where particles breed at a rate which depends on the number of neighboring particles. Under general assumptions on the breeding rates we prove the existence of a phase where the population…
Motivation: Over the past decade, network-based approaches have proven useful in identifying disease modules within the human interactome, often providing insights into key mechanisms and guiding the quest for therapeutic targets. This is…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $\lambda$. There is a threshold for $\lambda$, which is called $\lambda_w$, that separates almost sure global extinction from global…
Bio-inspired paradigms are proving to be useful in analyzing propagation and dissemination of information in networks. In this paper we explore the use of multi-type branching processes to analyse viral properties of content in a social…
Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies…
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
We investigate the number of topological ends of the trace of branching random walk (BRW) on a graph, giving a sufficient condition for the trace to have infinitely many ends. We then describe some interesting examples of non-symmetric BRWs…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…
Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…
We study a system of random walks, known as the frog model, starting from a profile of independent Poisson($\lambda$) particles per site, with one additional active particle planted at some vertex $\mathbf{o}$ of a finite connected simple…
Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.
Characterizing the occupation statistics of a radiation flow through confined geometries is key to such technological issues as nuclear reactor design and medical diagnosis. This amounts to assessing the distribution of the travelled length…
A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
In the present paper, we introduce and analyze elephant random walks (ERWs) on bipartite periodic lattices arising as coverings of dipole graphs. We focus on lattices whose admissible step directions in the two parts of the bipartition are…
This paper investigates the long-time behavior of double branching annihilating random walkers with nearest-neighbor dependent rates. The system consists of even number of particles which can execute nearest-neighbor random walk and they…