May 5, 2006: Jean Steiner, CIMS
HideandSeek and Spectral Invariants (on Markov Chains and Surfaces)
In this talk, I will describe a HideandSeek game that gives a
probabilistic interpretation of two tracelike spectral invariants. I
will begin by describing the Markov Chain setting, in which a classical
spectral invariant known as Kemeny's constant arises. I will then discuss
(a suitably modified) game that a Brownian particle might play on a
surface: here, the spectral invariant is a regularized 'trace' for the
Laplacian operator, which contains geometrical information.
