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

  • Khalil Chouk
  • Jan Gairing
  • Nicolas PerkowskiEmail author


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 Schrödinger 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.


Parabolic Anderson model Random polymer measure Random Schrödinger operator Invariance principle Paracontrolled distributions 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institut Für MathematikHumboldt-Universität zu BerlinBerlinGermany

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