
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
1p. 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.
