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Related papers: Branching Brownian motion with selection

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Motivated by the goal of understanding the evolution of populations undergoing selection, we consider branching Brownian motion in which particles independently move according to one-dimensional Brownian motion with drift, each particle may…

Probability · Mathematics 2021-02-04 Matthew I. Roberts , Jason Schweinsberg

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 study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a…

Statistical Mechanics · Physics 2015-06-15 Alexander K. Hartmann , Satya N. Majumdar , Alberto Rosso

We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate \beta > 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles…

Probability · Mathematics 2013-02-19 Sergey Bocharov , Simon C. Harris

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

Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion where each particle independently moves as Brownian motion…

Probability · Mathematics 2022-01-25 Jiaqi Liu , Jason Schweinsberg

We give a proof of a result on the growth of the number of particles along chosen paths in a branching Brownian motion. The work follows the approach of classical large deviations results, in which paths in $C[0,1]$ are rescaled onto…

Probability · Mathematics 2010-04-22 Simon Harris , Matthew Roberts

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

Information Theory · Computer Science 2008-06-09 Michael Chertkov , Lukas Kroc , Massimo Vergassola

Recently, we introduced the active Dyson Brownian motion model (DBM), in which $N$ run-and-tumble particles interact via a logarithmic repulsive potential in the presence of a harmonic well. We found that in a broad range of parameters the…

Statistical Mechanics · Physics 2024-11-08 Leo Touzo , Pierre Le Doussal , Gregory Schehr

The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at time $0$. The particle moves according to a Brownian motion…

Probability · Mathematics 2021-10-06 Xinxin Chen , Bastien Mallein

Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…

Physics Education · Physics 2007-05-23 Kasturi Basu , Kopinjol Baishya

Occupation time fluctuation limits of particle systems in R^d with independent motions (symmetric stable Levy process, with or without critical branching) have been studied assuming initial distributions given by Poisson random measures…

Probability · Mathematics 2012-03-14 Tomasz Bojdecki , Luis G. Gorostiza , Anna Talarczyk

We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the…

Probability · Mathematics 2025-11-18 Daniel Ahlberg , Omer Angel , Brett Kolesnik

We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift $-\mu$ and killed upon reaching $0$, starting with $N$ particles. More precisely, particles…

Probability · Mathematics 2024-06-04 Julie Tourniaire

Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at sub-micro scales, where inter-molecular diffusion and surface…

Fluid Dynamics · Physics 2025-02-26 Haodong Zhang , Fei Wang , Lorenz Ratke , Britta Nestler

We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and…

Probability · Mathematics 2019-03-19 Sergey Bocharov

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

Probability · Mathematics 2016-08-11 Miklós Z. Rácz , Mykhaylo Shkolnikov

Consider a system of infinitely many Brownian particles on the real line. At any moment, these particles can be ranked from the bottom upward. Each particle moves as a Brownian motion with drift and diffusion coefficients depending on its…

Probability · Mathematics 2016-09-06 Andrey Sarantsev

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…

Probability · Mathematics 2012-10-02 Ioannis Karatzas , Soumik Pal , Mykhaylo Shkolnikov

We consider the Fleming-Viot particle system consisting of $N$ identical particles evolving in $\mathbb{R}_{>0}$ as Brownian motions with constant drift $-1$. Whenever a particle hits $0$, it jumps onto another particle in the interior. It…

Probability · Mathematics 2023-06-07 Oliver Tough