Any renewal processes on N0 with a polynomial tail, with exponent α∈(0,1), has a non-trivial scaling limit, known as the α-stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i.i.d. random environment, called disordered pinning models. We show that for α∈12,1 these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subset of R in a white noise random environment, with subtle features:Any fixed a.s. property of the (Formula presented.)-stable regenerative set (e.g., its Hausdorff dimension) is also an a.s. property of the CDPM, for almost every realization of the environment.Nonetheless, the law of the CDPM is singular with respect to the law of the (Formula presented.)-stable regenerative set, for almost every realization of the environment. The existence of a disordered continuum model, such as the CDPM, is a manifestation of disorder relevance for pinning models with α∈12,1.
Caravenna, F., Sun, R., & Zygouras, N. (2016). The continuum disordered pinning model. PROBABILITY THEORY AND RELATED FIELDS, 164(1-2), 17-59 [10.1007/s00440-014-0606-4].
Citazione: | Caravenna, F., Sun, R., & Zygouras, N. (2016). The continuum disordered pinning model. PROBABILITY THEORY AND RELATED FIELDS, 164(1-2), 17-59 [10.1007/s00440-014-0606-4]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | Si | |
Titolo: | The continuum disordered pinning model | |
Autori: | Caravenna, F; Sun, R; Zygouras, N | |
Autori: | ||
Data di pubblicazione: | 2016 | |
Lingua: | English | |
Rivista: | PROBABILITY THEORY AND RELATED FIELDS | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00440-014-0606-4 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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