The maximum of branching random walk in spatially random branching environment

2017. 10. 26. 16:15
Jiri Cerny (Vienna)

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.