TALK BY PAT FITZSIMMONS, OCTOBER 14, 2010

TITLE: Kac's asymptotic scattering length via Kuznetsov measures

ABSTRACT: I will examine the "scattering length" Γ(V) of a non-negative integrable potential V in the context of a right Markov process X with distinguished excessive measure m:

A convenient epression for Γ(V) will be discussed. This expression yields immediately Kac's asymptotic formula
where Cap is the capacity associated with X and m, and F is the fine support of the CAF int0t V(Xs) ds.
This development parallels Spitzer's asymptotic formula for the distribution function of the hitting time of a set.