A localisation phase transition for the catalytic branching random walk
In this joint work with Bruno Schapira, we show the existence of a phase transition between a localisation and a non-localisation regime for a branching random walk with a catalyst at the origin. More precisely, we consider a continuous-time branching random walk that jumps at rate one, with simple random walk jumps on Z^d, and that branches (with binary branching) at rate λ>0 everywhere, except at the origin, where it branches at rate λ0>λ. We show that, if λ0 is large enough, then the occupation measure of the branching random walk localises (i.e. converges almost surely without spatial renormalisation), whereas, if λ0 is close enough to λ, then localisation cannot occur, at least not in a strong sense.
Date:
10 February 2025, 14:00
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue Details:
L4
Speaker:
Cecile Mailler (University of Bath)
Organising department:
Department of Statistics
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Members of the University only
Editor:
Julien Berestycki
