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CMS Jeffery-Williams Lecture / Conférence Jeffery-Williams de la
SMC
- EDWIN PERKINS, University of British Columbia
Super-Brownian motion and critical spatial stochastic systems
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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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