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The kinetics of annihilating random walks in one dimension, with the half-line x>0 initially filled, is investigated. The survival probability of the nth particle from the interface exhibits power-law decay, S_n(t)~t^{-alpha_n}, with…

Statistical Mechanics · Physics 2009-10-30 L. Frachebourg , P. L. Krapivsky , S. Redner

We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of…

Statistical Mechanics · Physics 2009-11-10 Boris M. Shipilevsky

We consider the symmetric simple exclusion system on $\mathbb{Z}^d$, $d \ge 2$, starting from a class of ``step'' initial conditions in which particles are constrained within a half-space. One may count the number $N_t$ of particles that…

Probability · Mathematics 2025-02-28 Michael Conroy , Sunder Sethuraman

We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where they are immediately absorbed. It is…

Probability · Mathematics 2018-09-13 Oren Louidor , Santiago Saglietti

The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…

Condensed Matter · Physics 2009-10-28 E. Ben-Naim , S. Redner , P. L. Krapivsky

We study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We focus on sparse initial conditions where…

Statistical Mechanics · Physics 2016-11-23 E. Ben-Naim , P. L. Krapivsky

We consider two species of particles performing random walks in a domain in $\mathbb{R}^d$ with reflecting boundary conditions, which annihilate on contact. In addition, there is a conservation law so that the total number of particles of…

Probability · Mathematics 2007-05-23 Krzysztof Burdzy , Jeremy Quastel

We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…

Statistical Mechanics · Physics 2015-06-25 S. Ispolatov , P. L. Krapivsky

Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas is studied in the framework of an exact analytic approach. For an initial symmetric three-velocity distribution, the problem can be solved exactly and it is…

Condensed Matter · Physics 2009-10-22 Michel Droz , Pierre-Antoine Rey , Laurent Frachebourg , Jarosław Piasecki

Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rate one. It is well-known that the right-most particle at time…

Probability · Mathematics 2024-06-10 Julien Berestycki , Jiaqi Liu , Bastien Mallein , Jason Schweinsberg

We consider a system of $N$ particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the…

Probability · Mathematics 2015-03-24 Jean Bérard , Pascal Maillard

We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the particles are given a critical drift towards…

Probability · Mathematics 2021-07-23 Pascal Maillard , Jason Schweinsberg

We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…

Probability · Mathematics 2017-09-13 Nina Gantert , Stefan Junk

Red and blue particles are placed in equal proportion through-out either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation occurs when particles with different colors meet. We compare…

Probability · Mathematics 2021-06-04 Irina Cristali , Yufeng Jiang , Matthew Junge , Remy Kassem , David Sivakoff , Grayson York

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…

Probability · Mathematics 2015-06-05 Tertuliano Franco , Pablo Groisman

We study the pairwise annihilation process $A+A\to$ inert of a number of random walkers, which originally are localized in a small region in space. The size of the colony and the typical distance between particles increases with time and,…

Statistical Mechanics · Physics 2007-05-23 Georg Foltin , Karin A. Dahmen , Nadav M. Shnerb

In the open circular billiard particles are placed initially with a uniform distribution in their positions inside a planar circular vesicle. They all have velocities of the same magnitude, whose initial directions are also uniformly…

Statistical Mechanics · Physics 2009-11-11 J. F. Stilck

We examine the dynamical properties of an exclusion process with creation and annihilation of particles in the framework of a phenomenological domain-wall theory, by scaling arguments and by numerical simulation. We find that the length-…

Statistical Mechanics · Physics 2009-11-10 Robert Juhasz , Ludger Santen

This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper…

Probability · Mathematics 2012-10-09 Siva Athreya , Jan Swart

We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed…

Probability · Mathematics 2026-03-17 Yuliy Baryshnikov , Alexander Stolyar