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7:30 pm, Wednesday, Jan 14, 2015
Fairmont Lounge, St. John's College 2111 Lower Mall, UBC
Random walks, Brownian motion, and Percolation
Martin T. Barlow
Mathematics, University of British Columbia
A fundamental problem in physics, chemistry, biology, neuroscience, and
computer science is - how do local interactions give rise to large scale
properties of physical systems? One fundamental model of this is
percolation (like that in a coffee percolator!). This can be modeled by
motion of a particle on a graph in which links in some lattice network
(ie., points connected by lines) are deleted randomly with probability
1-p. We then want to know - can something move from one part of the
network to another? This "percolation", or random motion on these
networks, has a phase transition - at one specific value of p, very large
clusters appear, inside which percolation can occur. Clusters have a
"fractal" behaviour, at or close to this critical point, and there are
many unsolved (and very hard) problems concerning percolation at
criticality.
To learn more please visit his
webpage.
Additional resources for this talk: slides and
video.
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