Jiri Cerny (Vienna): The maximum of branching random walk in spatially random branching environment

Branching branching random walk and Brownian motion have been the subject of intensive research recently. We consider branching random walk and investigate the effect of introducing a spatially random branching environment. We are primarily interested in the position of the maximum particle, for which we prove a CLT. Our result correspond, on an analytic level, to a CLT for the front of the solutions to a randomized Fisher-KPP equation, and also to a CLT for the parabolic Anderson model.