Finite size scaling for homogeneous pinning models

Abstract : Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to which a lot of attention has been paid both because they are very relevant for applications and because of their {\sl exactly solvable character}, while displaying a non-trivial phase transition (in fact, a localization transition). The order of the transition depends on the tail of the inter-arrival law of the underlying renewal and the transition is continuous when such a tail is sufficiently heavy: this is the case on which we will focus. The main purpose of this work is to give a mathematical treatment of the {\sl finite size scaling limit} of pinning models, namely studying the limit (in law) of the process close to criticality when the system size is proportional to the correlation length.
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Contributeur : Julien Sohier <>
Soumis le : mardi 7 avril 2009 - 12:11:19
Dernière modification le : mercredi 12 octobre 2016 - 01:03:48
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:10:20


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  • HAL Id : hal-00245242, version 2
  • ARXIV : 0802.1040



Julien Sohier. Finite size scaling for homogeneous pinning models. 2009. <hal-00245242v2>



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