The overlap distribution at two temperatures for the branching Brownian motion

The extremal process of two - speed branching Brownian motion ∗ Anton

We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is σ1 for s ≤ bt and σ2 when bt ≤ s ≤ t. In the case σ1 > σ2, the process is the concatenation of two BBM extremal processes, as expected. In the case σ1 < σ...

Hyperbolic branching Brownian motion

Hyperbolic branching Brownian motion is a branching di usion process in which individual particles follow independent Brownian paths in the hyperbolic plane H2, and undergo binary ssion(s) at rate ¿0. It is shown that there is a phase transition in : For 51=8 the number of particles in any compact region of H2 is eventually 0, w.p.1, but for ¿1=8 the number of particles in any open set grows to...

Slowdown for time inhomogeneous branching Brownian motion

We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but rather proportional to T . We conjecture that this is the worse case correction possible.

The Patched Brownian Motion Distribution

Branching Brownian Motion with “mild” Poissonian Obstacles

We study a spatial branching model, where the underlying motion is Brownian motion and the branching is affected by a random collection of reproduction blocking sets called mild obstacles. We show that the quenched local growth rate is given by the branching rate in the ‘free’ region . When the underlying motion is an arbitrary diffusion process, we obtain a dichotomy for the local growth that ...