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Introduction to Disordered Pinning Models

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2025)

Abstract

We introduce the disorder disordered version of the pinning models, both in their quenched and annealed version. We define the free energy of the model and show that also in this case a localization/delocalization transition takes place. Most of the results presented in this chapter may be considered as soft, but they are the result of a subtle, albeit possibly standard in statistical mechanics, way of combining convexity and super-additivity properties. These techniques are repeatedly used in the sequel of these notes.

Keywords

  • Free Energy
  • Partition Function
  • Correlation Length
  • Concentration Inequality
  • Random Polymer

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Correspondence to Giambattista Giacomin .

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© 2011 Springer-Verlag Berlin Heidelberg

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Giacomin, G. (2011). Introduction to Disordered Pinning Models. In: Disorder and Critical Phenomena Through Basic Probability Models. Lecture Notes in Mathematics(), vol 2025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21156-0_3

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