From: Kelli McGee \(Kelly Services Inc\) (a-kellim@microsoft.com)
Date: Mon Apr 05 2004 - 10:05:56 PDT
You are invited to attend...
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WHO: Yuval Peres
AFFILIATION: UC Berkeley, Visiting MSR
TITLE: STABLE MARRIAGE OF POISSON AND LEBESGUE
WHEN: Mon 4/19/2004
WHERE: 113/1159 Research Lecture Room, Microsoft Research
TIME: 3:30PM-5:00PM
HOST: Scott Sheffield and Jennifer Chayes
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ABSTRACT:
Given a point process M of intensity one in the plane, the well-known
Voronoi tesselation assigns a polygon (of different area) to each point
of M. The geometry of "fair" allocations (assigning unit area to each
point of M) is richer and more mysterious: see
http://www.math.ubc.ca/~holroyd/stable.html
There is a unique "fair" allocation that is "stable" in the sense of the
Gale-Shapley stable marriage problem, every point of M is assigned a
bounded region with finitely many components, but obtaining any(!) tail
estimate for the diameter of these regions is open. These allocations
arose from the continuum version of the "extra head" problem, studied by
Thorisson and Liggett. The original problem is to find in a sequence of
i.i.d. coins with heads probability $p$, one coin that landed heads so
that all other coins are still i.i.d. with heads probability $p$. [This
is possible without randomization only when $1/p$ is an integer].
Talk based on joint works with C. Hoffman and A. Holroyd.
BIO:
Yuval Peres graduated from the Hebrew University, Jerusalem in 1990. He
taught in Jerusalem, at Stanford and at Yale before settling at UC
Berkeley. Yuval works on random walks, Brownian motion, Mixing of Markov
chains, percolation, random spanning trees, point processes and random
polynomials. He enjoys working with Students and Postdocs. His favorite
quote is from his son Alon, who was overheard at age 6 asking a friend:
"Leo, do you have a religion?
You know, a religion, like Christian, or Jewish, or Mathematics....?"
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