Related papers: Localization for Branching Random Walks in Random …
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
Consider a critical nearest neighbor branching random walk on the $d$-dimensional integer lattice initiated by a single particle at the origin. Let $G_{n}$ be the event that the branching random walk survives to generation $n$. We obtain…
We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider a model in which the trap depth increases…
We have simulated the evolution of age structured populations whose individuals represented by their diploid genomes were distributed on a square lattice. The environmental conditions on the whole territory changed simultaneously in the…
We consider random walks in dynamic random environments which arise naturally as spatial embeddings of ancestral lineages in spatial locally regulated population models. In particular, as the main result, we prove the quenched central limit…
We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…
We consider the branching capacity of the range of a simple random walk on $\mathbb Z^d$, with $d \ge 5$, and show that it falls in the same universality class as the volume and the capacity of the range of simple random walks and branching…
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…
In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d \geq 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains…
For a random walk in an elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying the a ballisticity condition slightly weaker than condition (T'), We consider the probability of linear slowdown. We show an…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We…
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…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…