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.

Caravenna, F., Cottini, F. (2022). Gaussian limits for subcritical chaos. ELECTRONIC JOURNAL OF PROBABILITY, 27(none), 1-35 [10.1214/22-EJP798].

Gaussian limits for subcritical chaos

Caravenna, F
;
Cottini, F
2022

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.
Articolo in rivista - Articolo scientifico
central limit theorem; directed polymer in random environment; Edwards-Wilkinson fluctuations; KPZ equation; polynomial chaos; stochastic heat equation; Wiener chaos;
English
20-giu-2022
2022
27
none
1
35
81
open
Caravenna, F., Cottini, F. (2022). Gaussian limits for subcritical chaos. ELECTRONIC JOURNAL OF PROBABILITY, 27(none), 1-35 [10.1214/22-EJP798].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/396138
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