A Two Cities Theorem for the Parabolic Anderson Model

Abstract

The parabolic Anderson problem is the Cauchy problem for the heat equation ∂tu(t, z) = ∆u(t, z) + ξ(z)u(t, z) on (0,∞) × Z with random potential (ξ(z) : z ∈ Z). We consider independent and identically distributed potentials, such that the distribution function of ξ(z) converges polynomially at infinity. If u is initially localised in the origin, i.e., if u… (More)

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