Gaussian Limits for Subcritical Chaos

Abstract

We present a simple criterion, only based on second moment assumptions, for the convergence of polynomial or Wiener chaos to a Gaussian limit. We exploit this criterion to obtain new Gaussian asymptotics for the partition functions of two-dimensional directed polymers in the sub-critical regime, including a singular product between the partition function and the disorder. These results can also be applied to the KPZ and Stochastic Heat Equation. As a tool of independent interest, we derive an explicit chaos expansion which sharply approximates the logarithm of the partition function.

arXiv comment35 pages, 1 figure. Final version published in EJP

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Cited by in corpus (2)

• Multiplicative SHE limit of random walks in space-time random environments
• Fluctuations of Quadratic Chaos