NDLI: The continuum disordered pinning model

Content Provider	Springer Nature Link
Author	Zygouras, Nikos Caravenna, Francesco Sun, Rongfeng
Copyright Year	2014
Abstract	Any renewal processes on $${\mathbb {N}}_0$$ with a polynomial tail, with exponent $$\alpha \in (0,1)$$ , has a non-trivial scaling limit, known as the $$\alpha $$ -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 $$\alpha \in \left( \frac{1}{2}, 1\right) $$ these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subset of $${\mathbb {R}}$$ in a white noise random environment, with subtle features: Any fixed a.s. property of the $$\alpha $$ 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 $$\alpha $$ 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 $$\alpha \in \left( \frac{1}{2}, 1\right) $$ .
Ending Page	59
Page Count	43
Starting Page	17
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	1
Volume Number	164
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-12-17
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Disorder relevance Mathematical and Computational Biology Scaling limit Theoretical, Mathematical and Computational Physics Interacting random processes; statistical mechanics type models; percolation theory Probability Theory and Stochastic Processes Quantitative Finance Fell–Matheron topology Hausdorff metric Weak disorder Disordered systems (random Ising models, random SchrÃ¶dinger operators, etc.) Statistics for Business/Economics/Mathematical Finance/Insurance Pinning model Random polymer Operation Research/Decision Theory Wiener Chaos expansion Polymers
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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