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Polynomial chaos and scaling limits of disordered systems
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Caravenna, Francesco, Rongfeng, Sun and Zygouras, Nikos (2017) Polynomial chaos and scaling limits of disordered systems. Journal of the European Mathematical Society, 19 (1). pp. 1-65. doi:10.4171/JEMS/660 ISSN 1435-9855.
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Official URL: http://dx.doi.org/10.4171/JEMS/660
Abstract
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.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Journal of the European Mathematical Society | ||||||||
Publisher: | European Mathematical Society Publishing House | ||||||||
ISSN: | 1435-9855 | ||||||||
Official Date: | March 2017 | ||||||||
Dates: |
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Volume: | 19 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 1-65 | ||||||||
DOI: | 10.4171/JEMS/660 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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