Regenerative random permutations of integers

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.

30 pages. This paper is published by https://projecteuclid.org/euclid.aop/1556784022

References in corpus (5)

• Spatial random permutations and infinite cycles
• The Descent Set and Connectivity Set of a Permutation
• Renewal sequences and record chains related to multiple zeta sums
• Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees
• Gaps and interleaving of point processes in sampling from a residual allocation model

Cited by in corpus (4)

• On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking I
• A central limit theorem for descents of a Mallows permutation and its inverse
• The Mean of Multi-Object Trajectories
• Multivariable versions of a lemma of Kaluza's