# The longest excursion of a random interacting polymer

Source: [The longest excursion of a random interacting polymer](<https://www.sota2.com/research/paper/68fa4f071e209131ce96046c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:06:50.519Z

Authors: Janine K\\"ocher, Wolfgang K\\"onig

Published: 2011-03-01T16:54:22.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1103.0214>)

[PDF](<https://arxiv.org/pdf/1103.0214.pdf>)