Persistence probabilities for an integrated random walk bridge
  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. 
Frank Aurzada, Steffen Dereich, Mikhail Lifshits
math.PR