Asymptotic behavior of branching diffusion processes in periodic media
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We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, 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. A key ingredient in our analysis is a sharp estimate of the transition kernel for the branching process, valid up to linear in time distances from the location of the initial particle.
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Phillip Griffiths Assistant Research Professor
I am a Griffiths Assistant Research Professor at the Department of Mathematics at Duke University. Prior to arriving at Duke, I completed my Ph.D. from the Department of Mathematics at the University of Maryland. The main focus of my research is asymptotic problems arising from Branching Processes, Branching Diffusions and related Dynamical Systems.
Associate Professor of Mathematics
I study partial differential equations and probability, which have been used to model many phenomena in the natural sciences and engineering. In some cases, the parameters for a partial differential equation are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in differential equations modeling random phenomena and whether one can describe the statistical properties of solutions to these equations. Asymptotic anal
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