Sinai excursions

A random walk bridge is a Sinai excursion if its area process is an excursion. We find the precise asymptotic probability that a random walk is such an excursion, responding to a question of Caravenna and Deuschel, which arose in their study of random polymers exhibiting entropic repulsion. Joint work with Serte Donderwinkel, arXiv:2403.12941.