# Regenerative random permutations of integers

## TL;DR

This paper introduces regenerative permutations of integers, extending and unifying previous results on Mallows$(q)$ permutations, and explores three specific types: blocked, p-shifted, and p-biased permutations.

## Contribution

It proposes a new class of regenerative permutations that generalize Mallows$(q)$ permutations and analyzes three specific examples in detail.

## Key findings

- Recovered and extended results of Mallows$(q)$ permutations
- Analyzed properties of blocked, p-shifted, and p-biased permutations
- Established foundational theory for regenerative permutations

## Abstract

Motivated by recent studies of large 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 Mallows$(q)$ permutations are recovered and extended. Three special examples: blocked permutations, p-shifted permutations and p-biased permutations are studied.