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Title: Branching diffusion processes.

Abstract: We investigate the asymptotic behavior of solutions to parabolic partial differential equations 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. 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鈭抰h moment dominates the k鈭抰h 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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Meeting ID: 970 9325 9428

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