Related papers: Trimmed branching random walk and a free obstacle …
We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely the Run-and-Tumble particles. Notwithstanding the non-equilibrium character of these…
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 present a computational investigation of the mechanism governing size-based particle separation in microfluidic pinched flow fractionation. We study the behavior of particles moving through a pinching gap (i.e., a constriction in the…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
We investigate the asymptotic in $N$ of the mixing times of a Markov dynamics on $N-1$ ordered particles in an interval. This dynamics consists in resampling at independent Poisson times each particle according to a probability measure on…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle…
For a supercritical catalytic branching random walk on Z^d (d is positive integer) with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. Namely, we divide by t the position coordinates…
We consider the symmetric simple exclusion processes with a slow site in the discrete torus with $n$ sites. In this model, particles perform nearest-neighbor symmetric random walks with jump rates everywhere equal to one, except at one…
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 hydrodynamic behavior of some conservative particle systems with degenerate jump rates without exclusive constraints. More precisely, we study the particle systems without restrictions on the total number of particles per…
An intrinsic branching structure within the transient random walk on a strip in a random environment is revealed. As applications, which enables us to express the hitting time explicitly, and specifies the density of the absolutely…
We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to…
We use a macromodel of a flow-driven deterministic lateral displacement (DLD) microfluidic system to investigate conditions leading to size-separation of suspended particles. This model system can be easily reconfigured to establish an…
We study a non-reversible random walk advected by the symmetric simple exclusion process, so that the walk has a local drift of opposite sign when sitting atop an occupied or an empty site. We prove that the back-tracking probability of the…
We study the height of the maximal particle at time $t$ of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many intervals (obstacles) of order $t$. We obtain…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage…