From: Kelli McGee \(Kelly Services Inc\) (a-kellim@microsoft.com)
Date: Mon Apr 12 2004 - 15:47:18 PDT
You are invited to attend...
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WHO: Gordon Slade
AFFILIATION: University of British Columbia, Visiting MSR
TITLE: The phase transition for random subgraphs of the
n-cube
WHEN: Tue 4/27/2004
WHERE: 113/1021 Research Lecture Room, Microsoft Research
TIME: 3:30PM-5:00PM
HOST: Jennifer Chayes
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ABSTRACT:
The phase transition for random subgraphs of the complete graph has been
extensively studied since the pioneering work of Erdos and Renyi in
1960. In this talk, we describe several results which prove that in
many respects the phase transition for random subgraphs of general
high-dimensional transitive graphs is like the phase transition for the
complete graph. Our results are most far-reaching when the transitive
graph is the n-cube. In this case, which will be emphasized in the
talk, we also prove that the critical threshold has an asymptotic
expansion to all orders in 1/n, and we compute the first three terms of
the expansion. The talk is based on collaborations with Christian
Borgs, Jennifer Chayes, Remco van der Hofstad and Joel Spencer.
Preprints are available at http://www.math.ubc.ca/~slade .
BIO:
Gordon Slade is a Professor of Mathematics at the University of British
Columbia and a Visiting Researcher with the Theory Group at Microsoft
Research. His research is in the general areas of probability theory
and statistical mechanics. Much of his work uses an expansion method
known as the lace expansion to analyze high-dimensional systems.
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