central limit theorem; directed polymer in random environment; Edwards-Wilkinson fluctuations; KPZ equation; polynomial chaos; stochastic heat equation; Wiener chaos; Statistics and Probability; Statistics, Probability and Uncertainty
Résumé :
[en] 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.
Disciplines :
Mathématiques
Auteur, co-auteur :
Caravenna, Francesco; Università degli Studi di Milano, Bicocca, Italy
COTTINI, Francesca ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Università degli Studi di Milano, Bicocca, Italy
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