# The genealogy of branching Brownian motion with absorption

@article{Berestycki2010TheGO, title={The genealogy of branching Brownian motion with absorption}, author={Julien Berestycki and Nathanael Berestycki and Jason Schweinsberg}, journal={Annals of Probability}, year={2010}, volume={41}, pages={527-618} }

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. We show that the characteristic time scale for the evolution of this population is of order (logN) 3 , in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu’s continuous-state branching process…

## 83 Citations

### Branching Brownian motion in strip: survival near criticality

- Mathematics
- 2012

We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of…

### Particle configurations for branching Brownian motion with an inhomogeneous branching rate

- Mathematics
- 2021

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…

### Branching Brownian motion with selection of the N right-most particles: An approximate model

- Mathematics
- 2011

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 $N$…

### Title Critical branching Brownian motion with absorption : survival probability Permalink

- Mathematics
- 2012

We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of − √ 2. Kesten (1978)…

### Critical branching Brownian motion with absorption: survival probability

- Mathematics
- 2012

We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of $$-\sqrt{2}$$-2. Kesten…

### Branching Brownian motion with selection

- Mathematics
- 2012

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…

### A Strong Law of Large Numbers for Super-Critical Branching Brownian Motion with Absorption

- MathematicsJournal of Statistical Physics
- 2020

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…

### Critical branching Brownian motion with absorption: Particle configurations

- Mathematics
- 2012

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x > 0, particles move according to independent one-dimensional Brownian motions with…

### Yaglom-type limit theorems for branching Brownian motion with absorption

- MathematicsAnnales Henri Lebesgue
- 2022

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…

### The genealogy of an exactly solvable Ornstein–Uhlenbeck type branching process with selection

- Mathematics
- 2018

We study the genealogy of a solvable population model with N particles on the real line which evolves according to a discrete-time branching process with selection. At each time step, every particle…

## References

SHOWING 1-10 OF 72 REFERENCES

### Branching diffusion processes in population genetics

- MathematicsAdvances in Applied Probability
- 1976

A branching random field is considered as a model of either of two situations in genetics in which migration or dispersion plays a role. Specifically we consider the expected number of individuals NA…

### Maximal displacement of branching brownian motion

- Mathematics
- 1978

It is shown that the position of any fixed percentile of the maximal displacement of standard branching Brownian motion in one dimension is 21/2t–3 · 2−3/2 log t + O(1) at time t, the second-order…

### Stochastic flows associated to coalescent processes

- Mathematics
- 2003

Abstract. We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Möhle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models…

### Coalescents with multiple collisions

- Mathematics
- 1999

k−2 � 1 − xb−k � � dx� . Call this process a � -coalescent. Discrete measure-valued processes derived from the � -coalescent model a system of masses undergoing coalescent collisions. Kingman's…

### The general coalescent with asynchronous mergers of ancestral lines

- MathematicsJournal of Applied Probability
- 1999

Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral…

### Recent progress in coalescent theory

- PhysicsEnsaios Matemáticos
- 2009

Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of…

### The number of absorbed individuals in branching Brownian motion with a barrier

- Mathematics
- 2010

We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$. At the point $x > 0$, we add an absorbing barrier, i.e.\ individuals touching the…

### Multiplicative Martingales for Spatial Branching Processes

- Mathematics
- 1988

Out of simplicity, we restrict ourselves to consider the dyadic brownian branching process (Nt, t ∈ R+) on the real line. By definition of this process, its particles perform independent brownian…

### Survival probabilities for branching Brownian motion with absorption

- Mathematics
- 2007

We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-\rho$, undergo dyadic branching at rate $\beta>0$, and are killed on hitting the…