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We consider the random Schrödinger operator −ε −2 ∆ (d) + ξ (ε) (x), with ∆ (d) the discrete Laplacian on Z d and ξ (ε) (x) are bounded and independent random variables, on sets of the form D ε := {x ∈ Z d : xε ∈ D} for D bounded, open and with a smooth boundary, and study the statistics of the Dirichlet eigenvalues in the limit ε ↓ 0. Assuming Eξ (ε) (x) =(More)
We study two objects concerning the Wiener sausage among Poissonian obstacles. The first is the asymptotics for the replica overlap, which is the intersection of two independent Wiener sausages. We show that it is asymptotically equal to their union. This result confirms that the localizing effect of the media is so strong as to completely determine the(More)
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