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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 34, Fasc. 1,
pages 1 - 22
 

PERSISTENCE PROBABILITIES FOR A BRIDGE OF AN INTEGRATED SIMPLE RANDOM WALK

Frank Aurzada
Steffen Dereich
Mikhail Lifshits

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 random polymer models and proves a conjecture by Caravenna and Deuschel.

2000 AMS Mathematics Subject Classification: Primary: 60G50; Secondary: 60F99.

Keywords and phrases: Integrated random walk, local limit theorem, persistence probability.

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