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.

35 pages, 1 figure. Final version published in EJP

References in corpus (3)

• Central limit theorems for sequences of multiple stochastic integrals
• A forward-backward SDE from the 2D nonlinear stochastic heat equation
• Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erdös-Taylor theorem

Cited by in corpus (2)

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