Thomas Hughes (Bath)
Title: The extinction probability of rough super-Brownian motion.
Abstract: The rough super-Brownian motion (rSBM) is a super-Brownian motion with a white noise potential, and has been shown to arise as the scaling limit of branching random walks in random environments. In dimensions d鈮�2, its construction requires renormalization, in the sense of singular SPDEs. This talk concerns ongoing work on the short-time asymptotics of the extinction probability of the rSBM. This probability is characterized in terms of the maximal solution to a nonlinear singular SPDE, and I will discuss a construction of this solution via a perturbative expansion around the corresponding 鈥渘o noise鈥� solution. Time-permitting, I will also discuss the historical process associated to the rSBM and its connection to the directed polymer model.
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