Geodesic
Polynomial chaos and scaling limits of disordered systems
Journal of the European Mathematical Society, Tome 19 (2017) no. 1, pp. 1-65.

Voir la notice de l'article provenant de la source EMS Press

Inspired by recent work of Alberts, Khanin and Quastel, 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. 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 + 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 warrant further studies.
DOI : 10.4171/jems/660
Classification : 82-XX, 60-XX
Keywords: Continuum limit, finite size scaling, Lindeberg principle, polynomial chaos, Wiener chaos, disordered pinning model, directed polymer model, random field Ising model 
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Francesco Caravenna; Rongfeng Sun; Nikos Zygouras. Polynomial chaos and scaling limits of disordered systems. Journal of the European Mathematical Society, Tome 19 (2017) no. 1, pp. 1-65. doi : 10.4171/jems/660. http://geodesic.mathdoc.fr/articles/10.4171/jems/660/

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