### Abstract

We consider the model of a directed polymer pinned to a line of i.i.d. random charges, and focus on the interior of the delocalized phase. We first show that in this region, the partition function remains bounded. We then prove that for almost every environment of charges, the probability that the number of contact points in [0, n] exceeds clogn tends to 0 as n tends to infinity. The proofs rely on recent results of Birkner, Greven, den Hollander (2010) and Cheliotis, den Hollander (2010).

Original language | English (US) |
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Title of host publication | Seminaire de Probabilites XLIV |

Publisher | Springer Verlag |

Pages | 401-407 |

Number of pages | 7 |

ISBN (Print) | 9783642274602 |

DOIs | |

State | Published - 2012 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2046 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Mourrat, J. C. (2012). On the delocalized phase of the random pinning model. In

*Seminaire de Probabilites XLIV*(pp. 401-407). (Lecture Notes in Mathematics; Vol. 2046). Springer Verlag. https://doi.org/10.1007/978-3-642-27461-9_18