PERSISTENCE PROBABILITIES FOR A BRIDGE OF AN INTEGRATED
SIMPLE RANDOM WALK
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 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:
Keywords and phrases: Integrated random walk, local limit theorem, persistence