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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