Open Access
May 2019 Regenerative random permutations of integers
Jim Pitman, Wenpin Tang
Ann. Probab. 47(3): 1378-1416 (May 2019). DOI: 10.1214/18-AOP1286


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.


Download Citation

Jim Pitman. Wenpin Tang. "Regenerative random permutations of integers." Ann. Probab. 47 (3) 1378 - 1416, May 2019.


Received: 1 April 2017; Revised: 1 October 2017; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067272
MathSciNet: MR3945749
Digital Object Identifier: 10.1214/18-AOP1286

Primary: 05A05 , 60C05 , 60K05

Keywords: Bernoulli sieve , Cycle structure , indecomposable permutations , Mallows permutations , regenerative processes , renewal processes , size biasing

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 3 • May 2019
Back to Top