From: Kelli McGee \(Kelly Services Inc\) (a-kellim@microsoft.com)
Date: Fri Jul 09 2004 - 15:52:24 PDT
Updated Host: Jeong Han Kim.
________________________________
From: Kelli McGee (Kelly Services Inc)
Sent: Friday, July 09, 2004 8:37 AM
To: 'msrtalks@math.washington.edu'; 'theory-group@cs.washington.edu'
Cc: Kelli McGee (Kelly Services Inc)
Subject: 7/13/2004 The Giant Component; Joel Spencer, Courant Institute,
New York
You are invited to attend...
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WHO: Joel Spencer
AFFILIATION: Courant Institute, New York
TITLE: The Giant Component
WHEN: Tue 7/13/2004
WHERE: 113/1159 Research Lecture Room, Microsoft Research
TIME: 3:30PM-5:00PM
HOST: Jeong Han Kim
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ABSTRACT:
In 1960 Paul Erdos and Alfred Renyi showed that the random graph G(n,p)
with p=c/n and c>1 contained, with high probability, a "giant
component," whose size was roughly yn for an explicit y=y(c). We today
consider the phase transition at c=1 and the subcritical, c<1, and
supercritical, c>1, regimes as prime examples of percolation behavior.
We give a somewhat novel approach to examining the giant component. We
are able to derive the local joint distribution on the number of
vertices and edges of the giant component. Applying some reverse
engineering we are then able to find, in certain ranges, the asymptotics
for the number C(k,l) of connected labelled graphs on k vertices with
k-1+l edges.
BIO:
Joel Spencer is a Professor of Mathematics and Computer Science at the
Courant Institute, New York. His research centers on the intersection
of Discrete Mathematics, Theoretical Computer Science, and Probability.
His books include "The Probabilistic Method" (with Noga Alon) and "The
Strange Logic of Random Graphs." He is cofounder (with Michal Karonski)
of the journal Random Structures and Algorithms.
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