Cutoff for the asymmetric riffle shuffle

DOI10.1214/22-AOP1582zbMATH Open1500.60042arXiv2103.05068OpenAlexW3133839624MaRDI QIDQ2087390

Author name not available (Why is that?)

Publication date: 27 October 2022

Published in: (Search for Journal in Brave)

Abstract: In the Gilbert-Shannon-Reeds shuffle, a deck of $N$ cards is cut into two approximately equal parts which are then riffled uniformly at random. Bayer and Diaconis famously showed that this Markov chain undergoes cutoff in total variation after $frac3log(N)2log(2)$ shuffles. We establish cutoff for the more general asymmetric riffle shuffles in which one cuts the deck into differently sized parts before riffling. The value of the cutoff point confirms a conjecture of Lalley from 2000. Some appealing consequences are that asymmetry always slows mixing and that total variation mixing is strictly faster than separation and $L^{infty}$ mixing.

Full work available at URL: https://arxiv.org/abs/2103.05068

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Cutoff for the asymmetric riffle shuffle

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2087390)