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# Daniel Jerison : Random walks on sandpile groups

The sandpile group of a finite graph is an abelian group that is defined using the graph Laplacian. I will describe a natural random walk on this group. The main questions are: what is the mixing time of the sandpile random walk, and how is it affected by the geometry of the underlying graph? These questions can sometimes be answered even if the actual group is unknown. I will present an explicit characterization of the eigenvalues and eigenfunctions of the sandpile walk, and demonstrate an inverse relationship between the spectral gaps of the sandpile walk and the simple random walk on the underlying graph. This is joint work with Lionel Levine and John Pike.

**Category**: Probability**Duration**: 01:34:48**Date**: April 2, 2015 at 4:25 PM**Views**: 115-
**Tags:**seminar, Probability Seminar

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