# Brownian bees in the infinite swarm limit

@article{Berestycki2020BrownianBI, title={Brownian bees in the infinite swarm limit}, author={Julien Berestycki and Éric Brunet and James Nolen and Sarah Penington}, journal={The Annals of Probability}, year={2020} }

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 branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that as $N \to \infty$ the behaviour of the particle system is well approximated by the solution of a free boundary…

## 7 Citations

### Brownian Bees with Drift: Finding the Criticality

- Mathematics
- 2023

This dissertation examines the impact of a drift {\mu} on Brownian Bees, which is a type of branching Brownian motion that retains only the N closest particles to the origin. The selection effect in…

### Rank dependent branching-selection particle systems

- MathematicsElectronic Journal of Probability
- 2021

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 free boundary problem arising from branching Brownian motion with selection

- Mathematics
- 2020

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…

### Hydrodynamics of particle systems with selection via uniqueness for free boundary problems

- Mathematics
- 2020

We study an injection-branching-selection particle system on $\R$ at the hydrodynamic limit under arbitrarily varying injection and removal rates, where the corresponding free boundary problem (FBP)…

### Barycentric Brownian bees

- MathematicsThe Annals of Applied Probability
- 2022

We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in $d$ dimensions. The model consists of $N$ particles undergoing dyadic branching Brownian motion with…

### Conditions for existence and uniqueness of the inverse first-passage time problem applicable for L\'evy processes and diffusions

- Mathematics
- 2023

For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi>0$. For Markov processes we give…

### Selection principle for the Fleming-Viot process with drift $-1$

- Mathematics
- 2023

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…

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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…

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We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in $d$ dimensions. The model consists of $N$ particles undergoing dyadic branching Brownian motion with…