2003 Volume 39 Issue 2 Pages 365-392
We study asymptotic behavior of the spectrum of a Schrödinger type operator LVλ=L−λ2 V on the Wiener space as λ→∞. Here L denotes the Ornstein-Uhlenbeck operator and V is a nonnegative potential function which has finitely many zero points. For some classes of potential functions, we determine the divergence order of the lowest eigenvalue. Also tunneling effect is studied.
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