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arXiv · 1205.2895

Persistence probabilities for an integrated random walk bridge

Frank Aurzada·Steffen Dereich·Mikhail Lifshits
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Abstract

We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability $n^{-1/2}$ to stay positive. This question is motivated by so-called random polymer models and proves a conjecture by Caravenna and Deuschel.

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Frank Aurzada, Steffen Dereich, Mikhail Lifshits. 2012-05-13. Persistence probabilities for an integrated random walk bridge. https://arxiv.org/abs/1205.2895

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