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Localization for $(1+1)$-dimensional pinning models with $(\nabla + \Delta)$-interaction

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Localization for $(1+1)$-dimensional pinning models with $(\nabla + \Delta)$-interaction
2.	Creator	Author's name, affiliation, country	Francesco Caravenna; Università degli Studi di Padova
2.	Creator	Author's name, affiliation, country	Martin Borecki; TU Berlin
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Pinning Model; Polymer Model; Linear Chain Model; Phase Transition; Localization Phenomena; Gradient Interaction; Laplacian Interaction; Free Energy; Markov Chain
3.	Subject	Subject classification	60K35; 82B41; 60J05
4.	Description	Abstract	We study the localization/delocalization phase transition in a class of directed models for a homogeneous linear chain attracted to a defect line. The self-interaction of the chain is of mixed gradient and Laplacian kind, whereas the attraction to the defect line is of $\delta$-pinning type, with strength $\epsilon \ge 0$. It is known that, when the self-interaction is purely Laplacian, such models undergo a non-trivial phase transition: to localize the chain at the defect line, the reward $\epsilon$ must be greater than a strictly positive critical threshold $\epsilon_c > 0$. On the other hand, when the self-interaction is purely gradient, it is known that the transition is trivial: an arbitrarily small reward $\epsilon > 0$ is sufficient to localize the chain at the defect line ($\epsilon_c = 0$). In this note we show that in the mixed gradient and Laplacian case, under minimal assumptions on the interaction potentials, the transition is always trivial, that is $\epsilon_c = 0$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-11-02
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1584
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1584
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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