WIAS Preprint No. 1596, (2011)
The longest excursion of a random interacting polymer
Authors
- Köcher, Janine
- König, Wolfgang
ORCID: 0000-0002-7673-4364
2010 Mathematics Subject Classification
- 60F05 82D60
Keywords
- Free energy, interacting polymer, longest excursion, extreme value theory, renewal theory
DOI
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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