An invariance principle for the two-dimensional parabolic Anderson model with small potential

Khalil Chouk; Jan Gairing; Nicolas Perkowski

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arXiv · 1609.02471

An invariance principle for the two-dimensional parabolic Anderson model with small potential

Khalil Chouk·Jan Gairing·Nicolas Perkowski

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Abstract

We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a discrete random polymer measure, as well as a universality result for the spectrum of discrete random Schr\"odinger operators on large boxes with small potentials. Our proof is based on paracontrolled distributions and some basic results for multiple stochastic integrals of discrete martingales.

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Khalil Chouk, Jan Gairing, Nicolas Perkowski. 2016-09-08. An invariance principle for the two-dimensional parabolic Anderson model with small potential. https://arxiv.org/abs/1609.02471

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