Geodesic
Polynomial chaos and scaling limits of disordered systems
Journal of the European Mathematical Society, Tome 19 (2017) no. 1, pp. 1-65 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

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 
@article{JEMS_2017_19_1_a0,
     author = {Francesco Caravenna and Rongfeng Sun and Nikos Zygouras},
     title = {Polynomial chaos and scaling limits of disordered systems},
     journal = {Journal of the European Mathematical Society},
     pages = {1--65},
     year = {2017},
     volume = {19},
     number = {1},
     doi = {10.4171/jems/660},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/660/}
}
TY  - JOUR
AU  - Francesco Caravenna
AU  - Rongfeng Sun
AU  - Nikos Zygouras
TI  - Polynomial chaos and scaling limits of disordered systems
JO  - Journal of the European Mathematical Society
PY  - 2017
SP  - 1
EP  - 65
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/660/
DO  - 10.4171/jems/660
ID  - JEMS_2017_19_1_a0
ER  - 
%0 Journal Article
%A Francesco Caravenna
%A Rongfeng Sun
%A Nikos Zygouras
%T Polynomial chaos and scaling limits of disordered systems
%J Journal of the European Mathematical Society
%D 2017
%P 1-65
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/660/
%R 10.4171/jems/660
%F JEMS_2017_19_1_a0
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

Cité par Sources :