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The longest excursion of a random interacting polymer
Preprint
01 March 2011
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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.