Related papers: Population Stabilization in Branching Brownian Mot…
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 the critical drift of $-\sqrt{2}$, and…
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 they are immediately absorbed. It is…
We consider branching Brownian motion in which initially there is one particle at $x$, particles produce a random number of offspring with mean $m+1$ at the time of branching events, and each particle branches at rate $\beta = 1/2m$.…
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 $-\sqrt{2}$. Kesten (1978) showed that almost surely this process…
We study a dyadic branching Brownian motion on the real line with absorption at 0, drift $\mu \in \mathbb{R}$ and started from a single particle at position $x>0.$ When $\mu$ is large enough so that the process has a positive probability of…
Consider a system of particles performing branching Brownian motion with negative drift $\mu = \sqrt{2 - \epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with…
We consider the limiting extremal process ${\mathcal X}$ of the particles of the binary branching Brownian motion. We show that after a shift by the logarithm of the derivative martingale $Z$, the rescaled "density" of particles, which are…
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 the interval shrinks to the critical value…
We study the order statistics of one dimensional branching Brownian motion in which particles either diffuse (with diffusion constant $D$), die (with rate $d$) or split into two particles (with rate $b$). At the critical point $b=d$ which…
Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rate one. It is well-known that the right-most particle at time…
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 analytically the order and gap statistics of particles at time $t$ for the one dimensional branching Brownian motion, conditioned to have a fixed number of particles at $t$. The dynamics of the process proceeds in continuous time…
It is well-known that the maximal particle in a branching Brownian motion sits near $\sqrt2 t - \frac{3}{2\sqrt2}\log t$ at time $t$. One may then ask about the paths of particles near the frontier: how close can they stay to this critical…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
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 slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift $-\sqrt{2+2\varepsilon}$, undergo dyadic fission at rate $1$, and are killed when they reach the origin. We…
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 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 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…
We consider a branching Brownian motion in $\mathbb{R}^2$ in which particles independently diffuse as standard Brownian motions and branch at an inhomogeneous rate $b(\theta)$ which depends only on the angle $\theta$ of the particle. We…