相关论文: Brunet-Derrida particle systems, free boundary pro…

We introduce and analyse a two-sided branching-selection particle system which generalises the well-known $N$-particle branching Brownian motion ($N$-BBM) model, which we call the $(N,p)$-BBM, where either the leftmost or rightmost particle…

We consider a branching-selection particle system on $\Z$ with $N \geq 1$ particles. During a branching step, each particle is replaced by two new particles, whose positions are shifted from that of the original particle by independently…

The $N$-branching Brownian motion with selection ($N$-BBM) is a particle system consisting of $N$ independent particles that diffuse as Brownian motions in $\mathbb{R}$, branch at rate one, and whose size is kept constant by removing the…

The Branching Brownian Motions (BBM) are particles performing independent Brownian motions in $\mathbb R$ and each particle at rate 1 creates a new particle at her current position; the newborn particle increments and branchings are…

We introduce particle systems in one or more dimensions in which particles perform branching Brownian motion and the population size is kept constant equal to $N > 1$, through the following selection mechanism: at all times only the $N$…

The Brownian bees model is a branching particle system with spatial selection. It is a system of $N$ particles which move as independent Brownian motions in $\mathbb{R}^d$ and independently branch at rate 1, and, crucially, at each…

We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…

We consider a class of branching-selection particle systems on $\R$ similar to the one considered by E. Brunet and B. Derrida in their 1997 paper "Shift in the velocity of a front due to a cutoff". Based on numerical simulations and…

In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number of particles with expectation greater…

We study a system of branching Brownian motions on $\mathbb R$ with annihilation: at each branching time a new particle is created and the leftmost one is deleted. In [7] it has been studied the case of strictly local creations (the new…

We present an approximation to the Brunet--Derrida model of supercritical branching Brownian motion on the real line with selection of the $N$ right-most particles, valid when the population size $N$ is large. It consists of introducing a…

We study a particle system with the following diffusion-branching-selection mechanism. Particles perform independent one dimensional Brownian motions and on top of that, at a constant rate, a pair of particles is chosen uniformly at random…

We consider a large family of branching-selection particle systems. The branching rate of each particle depends on its rank and is given by a function $b$ defined on the unit interval. There is also a killing measure $D$ supported on the…

We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…

We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…

This paper studies a branching-selection model of motionless particles in $\mathbb{R}^d$, with nonlocal branching, introduced by Durrett and Remenik in dimension $1$. The assumptions on the fitness function, $F$, and on the inhomogeneous…

Consider $N$ particles performing random walks on the $\epsilon$-grid $(\epsilon Z)^d$, $\epsilon>0$ with branching and density-dependent selection: When one of the particles branches, a particle is removed from the most populated site. The…

We study a system consisting of $n$ particles, moving forward in jumps on the real line. Each particle can make both independent jumps, whose sizes have some distribution, or ``synchronization'' jumps, which allow it to join a randomly…

We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the…

We consider a reaction-diffusion system of densities of two types of particles, introduced by Edouard Hannezo et al. in the context of branching morphogenesis. It is a simple model for a growth process: active, branching particles form the…