Inspired by recent work of Alberts, Khanin and Quastel [AKQ14a], we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable, given by a Wiener chaos expansion over the d-dimensional white noise. A key ingredient in our approach is a Lindeberg principle for polynomial chaos expansions, which extends earlier work of Mossel, O'Donnell and Oleszkiewicz [MOO10]. These results provide a unified framework to study the continuum and weak disorder scaling limits of statistical mechanics systems that are disorder relevant, including the disordered pinning model, the (long-range) directed polymer model in dimension 1 C 1, and the two-dimensional random field Ising model. This gives a new perspective in the study of disorder relevance, and leads to interesting new continuum models that deserve further studies.

Caravenna, F., Sun, R., Zygouras, N. (2017). Polynomial chaos and scaling limits of disordered systems. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 19(1), 1-65 [10.4171/JEMS/660].

Polynomial chaos and scaling limits of disordered systems

CARAVENNA, FRANCESCO;
2017

Abstract

Inspired by recent work of Alberts, Khanin and Quastel [AKQ14a], we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable, given by a Wiener chaos expansion over the d-dimensional white noise. A key ingredient in our approach is a Lindeberg principle for polynomial chaos expansions, which extends earlier work of Mossel, O'Donnell and Oleszkiewicz [MOO10]. These results provide a unified framework to study the continuum and weak disorder scaling limits of statistical mechanics systems that are disorder relevant, including the disordered pinning model, the (long-range) directed polymer model in dimension 1 C 1, and the two-dimensional random field Ising model. This gives a new perspective in the study of disorder relevance, and leads to interesting new continuum models that deserve further studies.
Articolo in rivista - Articolo scientifico
Continuum limit; Directed polymer model; Disordered pinning model; Finite size scaling; Lindeberg principle; Polynomial chaos; Random field Ising model; Wiener chaos; Mathematics (all); Applied Mathematics
English
2017
19
1
1
65
reserved
Caravenna, F., Sun, R., Zygouras, N. (2017). Polynomial chaos and scaling limits of disordered systems. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 19(1), 1-65 [10.4171/JEMS/660].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/152379
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