Wednesday, January 31, 3:30.

Holly Carley

	Large Deviations: Cramer's theorem and Gibb's Conditioning Principle

This will be the first of a series of teaching/research seminars on
large deviations.  We will begin with Cramer's theorem for sums of
independent random variables, then go on to problems for diffusions, e.g.,
Schilder's theorem.  We will be interested in the problem of
developing higher asymptotics.






Friday, February 2, at 3:30 pm: in 228 Kerchof Hall

Dana Randall (Georgia Institute of Technology)

            Sampling Adsorbing Staircase Walks 
        Using a New Markov Chain Decomposition Method

Staircase walks are lattice paths from (0,0) to (2n,0)
which take diagonal steps and which never fall below the x-axis.
A path hitting the x-axis k times is assigned a weight of c^k,
where c > 0.  A simple local Markov chain which connects
the state space and converges to the Gibbs measure (which normalizes
these weights) is known to be rapidly mixing when c = 1, and can
easily be shown to be rapidly mixing when c < 1.  We give the
first proof that this Markov chain is also mixing in the more
interesting case of c > 1, known in the statistical physics
community as ``adsorbing staircase walks.''  The main new
ingredient is a decomposition technique which allows us to analyze the
Markov chain in pieces, applying different arguments to analyze
each piece.

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Arrive Wednesday afternoon
CS Colloquium Thursday afternoon
MathPhys talk Friday afternoon
Leave Saturday morning
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