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TALK BY PAT FITZSIMMONS, OCTOBER 14, 2010
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TITLE: Kac's asymptotic scattering length via Kuznetsov measures
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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*:

Γ(*V*) := lim _{t --> infinity} *t*^{-1}E^{m}
[1-exp(-int_{0}^{t} *V*(*X*_{s}) d*s*)].

A convenient epression for Γ(*V*) will be discussed. This expression yields immediately Kac's asymptotic formula

lim _{λ --> infinity} Γ(λ*V*) = Cap(F),

where Cap is the capacity associated with *X* and *m*, and *F* is the fine support of the CAF
int_{0}^{t} *V*(*X*_{s}) d*s*.

This development parallels Spitzer's asymptotic formula for the distribution function of the hitting time of a set.