We consider disordered systems of a directed polymer type, for which disorder is so-called marginally relevant. These include the usual (short-range) directed polymer model in dimension (2 + 1), the long-range directed polymer model with Cauchy tails in dimension (1 + 1) and the disordered pinning model with tail exponent 1/2. We show that in a suitable weak disorder and continuum limit, the partition functions of these different models converge to a universal limit: a log-normal random field with a multi-scale correlation structure, which undergoes a phase transition as the disorder strength varies. As a by-product, we show that the solution of the two-dimensional stochastic heat equation, suitably regularized, converges to the same limit. The proof, which uses the celebrated fourth moment theorem, reveals an interesting chaos structure shared by all models in the above class
Caravenna, F., Sun, R., & Zygouras, N. (2017). Universality in marginally relevant disordered systems. THE ANNALS OF APPLIED PROBABILITY, 27(5), 3050-3112 [10.1214/17-AAP1276].
Citazione: | Caravenna, F., Sun, R., & Zygouras, N. (2017). Universality in marginally relevant disordered systems. THE ANNALS OF APPLIED PROBABILITY, 27(5), 3050-3112 [10.1214/17-AAP1276]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | Si | |
Titolo: | Universality in marginally relevant disordered systems | |
Autori: | Caravenna, F; Sun, R; Zygouras, N | |
Autori: | ||
Data di pubblicazione: | 2017 | |
Lingua: | English | |
Rivista: | THE ANNALS OF APPLIED PROBABILITY | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1214/17-AAP1276 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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