Abstract
We removem-balls of centersw 1,...,w m with the same radius α/m from a bounded domain Ω inR 3 with smooth boundary γ. Let μ k (α/m;w(m)) denote thek-th eigenvalue of the Laplacian in Ω/m-balls under the Dirichlet condition. We consider μ k (α/m;w(m)) as a random variable on a probability space (w 1,...,w m)∈Ω × ... × Ω and we examine a precise behaviour of μ k (α/m;w(m)) asm → ∞. We give an elaboration of. M. Kac's theorem.
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