Bastien Mallein

Branching random walk with selection at critical rate

We consider a branching-selection particle system on the real line. In this model the total size of the population at time

Maximal displacement of a branching random walk in time-inhomogeneous environment

n

Maximal displacement in a branching random walk through interfaces

is limited by

Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment

\exp\left(a n^{1/3}\right)

Maximal displacement in the

. At each step

d

n

-dimensional branching Brownian motion

, every individual dies while reproducing independently, making children around their current position according to i.i.d. point processes. Only the

Second order behavior of the block counting process of beta coalescents

\exp\left(a(n+1)^{1/3}\right)

N -Branching random walk with α-stable spine

rightmost children survive to form the

Brownian motion and random walk above quenched random wall

(n+1)^\mathrm{th}