OxTalks will soon move to the new Halo platform and will become 'Oxford Events.' There will be a need for an OxTalks freeze. This was previously planned for Friday 14th November – a new date will be shared as soon as it is available (full details will be available on the Staff Gateway).
In the meantime, the OxTalks site will remain active and events will continue to be published.
If staff have any questions about the Oxford Events launch, please contact halo@digital.ox.ac.uk
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.
