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Related papers: Annihilating branching Brownian motion

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Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with…

Probability · Mathematics 2022-09-21 Darío Cruzado Padró , Matthew Junge , Lily Reeves

We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of the coalescing Brownian motions. The main difference is that…

Probability · Mathematics 2017-02-21 Vitalii Konarovskyi

We consider a stochastic process that describes several particles interacting by either merging or annihilation. When two particles merge, they combine their masses; when annihilation occurs, only the particle of smallest mass survives.…

Probability · Mathematics 2017-09-25 Antonio Auffinger , Dylan Cable

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

Systems of instantaneously annihilating or coalescing Brownian motions on the line are considered. The extreme points of the set of entrance laws for this process are shown to be Pfaffian point processes at all times and their kernels are…

Probability · Mathematics 2026-02-19 Roger Tribe , Oleg Zaboronski

We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly…

Probability · Mathematics 2025-11-04 Sungwon Ahn , Matthew Junge , Hanbaek Lyu , Lily Reeves , Jacob Richey , David Sivakoff

We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…

Probability · Mathematics 2014-09-09 Vadim Gorin , Mykhaylo Shkolnikov

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

A class of interacting particle systems on $\mathbb{Z}$, involving instantaneously annihilating or coalescing nearest neighbour random walks, are shown to be Pfaffan point processes for all deterministic initial conditions. As diffusion…

Probability · Mathematics 2019-03-26 Barnaby Garrod , Mihail Poplavskyi , Roger Tribe , Oleg Zaboronski

We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles.…

Probability · Mathematics 2013-03-15 Julien Berestycki , Nathanaël Berestycki , Jason Schweinsberg

We investigate the behaviour of a chain of interacting Brownian particles with one end fixed and the other moving away at slow speed, in the limit of small noise. The interaction between particles is through a pairwise potential with finite…

Probability · Mathematics 2010-07-20 Michael Allman , Volker Betz , Martin Hairer

Infinitely many particles of two types ("plus" and "minus") jump randomly along the one-dimensional lattice $\mathbf{Z}_{\varepsilon}=\varepsilon\mathbf{Z}$. Annihillations occur when two particles of different time occupy the same site.…

Mathematical Physics · Physics 2012-04-17 V. A. Malyshev , A. D. Manita

We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…

Probability · Mathematics 2018-03-29 Sergey Bocharov , Li Wang

We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e. each Brownian particle can convert internal energy to mechanical energy of motion. We assume the…

Statistical Mechanics · Physics 2011-08-11 Alexander Gluck , Helmuth Huffel , Sasa Ilijic

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…

Statistical Mechanics · Physics 2009-10-31 K. Mussawisade , J. E. Santos , G. M. Schütz , ;

Consider a finite system of Brownian particles on the real line. Each particle has drift and diffusion coefficients depending on its current rank relative to other particles, as in Karatzas, Pal and Shkolnikov (2012). We prove some…

Probability · Mathematics 2016-05-24 Andrey Sarantsev

In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent Brownian motion, but only K $\ge$ 1 particles on the far…

Analysis of PDEs · Mathematics 2025-05-14 Mete Demircigil , Milica Tomasevic

The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…

Probability · Mathematics 2024-04-12 Alexander M. G. Cox , Emma Horton , Denis Villemonais

Directed transport of interacting active (self-propelled)Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed…

Statistical Mechanics · Physics 2015-05-12 Bao-quan Ai , Ya-feng He , Wei-rong Zhong

We consider finite systems of interacting Brownian particles including active friction in the framework of nonlinear dynamics and statistical/stochastic theory. First we study the statistical properties for $1-d$ systems of masses connected…

Statistical Mechanics · Physics 2007-05-23 Werner Ebeling