Convergence of branching transport processes to branching brownian motion

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...

Occupation Time Large Deviations for Critical Branching Brownian Motion, Super-brownian Motion and Related Processes

We derive a large deviation principle for the occupation time functional, acting on functions with zero Lebesgue integral, for both superBrownian motion and critical branching Brownian motion in three dimensions. Our technique, based on a moment formula of Dynkin, allows us to compute the exact rate functions, which differ for the two processes. Obtaining the exact rate function for the super-B...

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.

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 ...

A Preliminary Investigation of Transport-branching Processes