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Persistence probabilities for a bridge of an integrated simple random walk

Aurzada F., Dereich S., Lifshits M.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 1

1--22

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.