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A random walk proof of Kirchhoff's matrix tree theorem

Date: 
Wednesday 17th June 2015 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Kirchhoff's matrix tree theorem relates the number of spanning trees in a graph to the determinant of a matrix derived from the graph. There are a number of proofs of Kirchhoff's theorem known, most of which are combinatorial in nature. In this talk we will present a relatively elementary random walk-based proof of Kirchhoff's theorem due to Greg Lawler which follows from his proof of Wilson's algorithm. Moreover, these same ideas can be applied to other computations related to general Markov chains and processes on a finite state space. Based in part on joint work with Larissa Richards (Toronto) and Dan Stroock (MIT).
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons