Probability Seminar
Thursday, September 26, 2019, 3:15pm, 119 Physics
Pratima Hebbar (Duke)
Branching diffusion processes in periodic media
Abstract:- We investigate the asymptotic behavior of solutions to parabolic partial differential equations (PDEs) in R^d with space-periodic diffusion matrix, drift, and potential. Using this asymptotics, we describe the behavior of branching diffusion processes in periodic media. In particular, for a super-critical branching process in periodic media, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k−th moment dominates the k−th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge.
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