Regenerative random permutations of integers

Abstract

Motivated by recent studies of large $\operatorname{Mallows}(q)$ permutations, we propose a class of random permutations of $\mathbb{N}_{+}$ and of $\mathbb{Z}$, called regenerative permutations. Many previous results of the limiting $\operatorname{Mallows}(q)$ permutations are recovered and extended. Three special examples: blocked permutations, $p$-shifted permutations and $p$-biased permutations are studied.