TALK BY PAT FITZSIMMONS, OCTOBER 14, 2010
TITLE: Kac's asymptotic scattering length via Kuznetsov measures
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:
Γ(V) := lim t --> infinity t-1Em
[1-exp(-int0t V(Xs) ds)].
A convenient epression for Γ(V) will be discussed. This expression yields immediately Kac's asymptotic formula
lim λ --> infinity Γ(λV) = Cap(F),
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.