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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.