Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model

Jörg Martin; Nicolas Perkowski

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arXiv · 1704.08653

Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model

Jörg Martin·Nicolas Perkowski

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Abstract

We develop a discrete version of paracontrolled distributions as a tool for deriving scaling limits of lattice systems, and we provide a formulation of paracontrolled distribution in weighted Besov spaces. Moreover, we develop a systematic martingale approach to control the moments of polynomials of i.i.d. random variables and to derive their scaling limits. As an application, we prove a weak universality result for the parabolic Anderson model: We study a nonlinear population model in a small random potential and show that under weak assumptions it scales to the linear parabolic Anderson model.

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Jörg Martin, Nicolas Perkowski. 2017-04-27. Paracontrolled distributions on Bravais lattices and weak universality of the 2d parabolic Anderson model. https://arxiv.org/abs/1704.08653

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