Tied-down occupation times of infinite ergodic transformations

Abstract

We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting random variables include the local times of $p$-stable L\'evy-bridges ($1<p\le 2$) and the transformations involved exhibit "tied-down renewal mixing" properties which refine rational weak mixing. Periodic local limit theorems for Gibbs-Markov and AFU maps are also established.