Related papers: First-passage competition with different speeds: p…
We derive the asymptotic first passage time (FPT) distribution for space-dependent variable-order time-fractional diffusion, where the fractional exponent $\alpha(x)$ varies with position. For any sufficiently smooth $\alpha(x)$ on a finite…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states…
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected,…
We investigate the survival probability of a particle diffusing between two parallel reflecting planes toward a periodic array of absorbing pillars. We approximate the periodic cell of this system by a cylindrical tube containing a single…
The statistics of the slowest first-passage time among a large population of $N$ searchers is crucial for determining the completion time of many stochastic processes. Classical extreme-value theory predicts that for diffusing particles in…
We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment, focusing on whether a population already established in one patch either successfully invades an adjacent empty…
A transient stochastic process is considered strongly transient if conditioned on returning to the starting location, the expected time it takes to return the the starting location is finite. We characterize strong transience for a…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
We study the competition and the evolution of nodes embedded in Euclidean restricted spaces. The population evolves by a branching process in which new nodes are generated when up to two new nodes are attached to the previous ones at each…
We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a spherically symmetric setting. This free boundary…
We consider long-range percolation on $\mathbb{Z}^d$, where the probability that two vertices at distance $r$ are connected by an edge is given by $p(r)=1-\exp[-\lambda(r)]\in(0,1)$ and the presence or absence of different edges are…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
First passage percolation on $\mathbb{Z}^2$ is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage…
Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…
We obtain two-sided bounds for the density of stochastic processes satisfying a weak H\"ormander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various…