A two cities theorem for the parabolic Anderson model.

By Wolfgang Konig, H. Lacoin, Peter Morters, N. Sidorova. 2011

60 citations recorded by the source corpus.

The parabolic Anderson problem is the Cauchy problem for the heat equation partial derivative(t)u(t, z) = Delta u(t,z) + xi(z)u(t,z) on (0,infinity) x Z(d) with random potential (xi(z): z is an element of Z(d)). We consider independent and identically distributed potentials, such that the distribution function of (z) converges polynomially at infinity. If u is initially localized in the origin, that is, if u(0, z) = 1(0)(z), we show that, as time goes to infinity, the solution is completely localized in two points almost surely and in one point with high probability. We also identify the asymptotic behavior of the concentration sites in terms of a weak limit theorem.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/779f257666524c262d4ca5874c7e85cfdbfdf1bd

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Citations in the corpus

Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency (2014, background): “g [12, 13, 14, 18, 31]), and as a localization property for the polymer measure [7].”