WIAS Preprint No. 1596, (2011)

The longest excursion of a random interacting polymer



Authors

  • Köcher, Janine
  • König, Wolfgang

2010 Mathematics Subject Classification

  • 60F05 82D60

Keywords

  • Free energy, interacting polymer, longest excursion, extreme value theory, renewal theory

Abstract

We consider a random $N$-step polymer under the influence of an attractive interaction with the origin and derive a limit law -- after suitable shifting and norming -- for the length of the longest excursion towards the Gumbel distribution. The embodied law of large numbers in particular implies that the longest excursion is of order $log N$ long. The main tools are taken from extreme value theory and renewal theory.

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