From: Kelli McGee \(Kelly Services Inc\) (a-kellim@microsoft.com)
Date: Fri May 07 2004 - 09:44:17 PDT
You are invited to attend...
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WHO: Russell Lyons
AFFILIATION: Indiana University
TITLE: Asymptotic Enumeration of Spanning Trees via Traces
and Random Walks
WHEN: Mon 5/24/2004
WHERE: 113/1021 Research Lecture Room, Microsoft Research
TIME: 3:30PM-5:00PM
HOST: Oded Schramm
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ABSTRACT:
Methods of enumeration of spanning trees in a finite graph and relations
to various areas of mathematics and physics have been investigated for
more than 150 years. We will review the history and applications. Then
we will give new formulas for the asymptotics of the number of spanning
trees of a graph. A special case answers a question of McKay (1983) for
regular graphs. The general answer involves a quantity for infinite
graphs that we call ``tree entropy", which we show is a logarithm of a
normalized determinant of the graph Laplacian for infinite graphs.
Proofs involve new traces and the theory of random walks.
BIO:
Russell Lyons got his Ph.D. in 1983 from the University of Michigan in
harmonic analysis. Several years later, he switched to probability
theory. His areas of research now include random walks, models from
statistical mechanics, trees, and determinantal probability measures.
He has had several research fellowships and teaches at Indiana
University.
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