Caravenna, Francesco, Rongfeng, Sun and Zygouras, Nikos (2014) The continuum disordered pinning model. Probability Theory and Related Fields, 164 (1). pp. 17-59. doi:10.1007/s00440-014-0606-4 ISSN 0178-8051.

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Abstract

Any renewal processes on N 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∈(1/2,1) 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 α-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 α-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∈(1/2,1)

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Probabilities
Journal or Publication Title:	Probability Theory and Related Fields
Publisher:	Springer Berlin Heidelberg
ISSN:	0178-8051
Official Date:	17 December 2014
Dates:	Date Event 17 December 2014 Published 19 June 2014 Submitted
Volume:	164
Number:	1
Page Range:	pp. 17-59
DOI:	10.1007/s00440-014-0606-4
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	12 August 2016
Date of first compliant Open Access:	12 August 2016
Funder:	European Research Council (ERC), Singapore. Ministry of Education. , Engineering and Physical Sciences Research Council (EPSRC), Marie Curie International Reintegration Grants (IRG)
Grant number:	267356 VARIS (ERC), AcRF Tier 1 Grant R-146-000-148-112, EP/L012154/1 (EPSRC), IRG-246809

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