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Comité de coordination


CMS Jeffery-Williams Lecture / Conférence Jeffery-Williams de la SMC

EDWIN PERKINS, University of British Columbia
Super-Brownian motion and critical spatial stochastic systems

Brownian motion arises as a universal limiting object for small centralized fluctuations. In the same way super-Brownian motion arises as a universal limiting object for nonnegative spatial stochastic systems near criticality. The list of stochastic systems which approach super-Brownian motion under rescaling includes distributions of genotypes undergoing random genetic drift and mutation, stochastic models for epidemic spread (contact processes) near criticality, competing species models in mathematical ecology (including the voter model), and percolation models at criticality and in sufficiently high dimensions. Some of these connections will be presented and discussed. In the unlikely event that there is time, we will then describe the current state of Itô's program for super-Brownian motion. That is, the study of interactive systems which behave locally as super-Brownian motion.


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