The longest excursion of a random interacting polymer

Janine Köcher; Wolfgang König

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arXiv · 1103.0214

The longest excursion of a random interacting polymer

Janine Köcher·Wolfgang König

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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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Janine Köcher, Wolfgang König. 2011-03-01. The longest excursion of a random interacting polymer. https://arxiv.org/abs/1103.0214

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