Random shuffles and group representations
type: Item
instance of: scholarly article
title: Random shuffles and group representations
zbMATH Open document ID: 0564.60007
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: The authors consider random walks on a finite group G with a uniform initial distribution, and ask for the distribution of the number T of steps it takes to reach a particular element of G, which may be assumed to be the unit of G. They obtain a formula for the generating function of T, involving the irreducible representations of G. These problems were motivated by questions on card shuffling. If one starts with a deck of n cards in random order and reshuffles it by choosing two cards at random and interchanging them, how long does it take that the deck is fully sorted? It turns out that the expected number of shuffles is \(n!+2(n-2)!+o((n-2)!)\). The paper also studies limit laws for T and other related results.
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 3899830
zbMATH Keywords: random walks on a finite group
zbMATH Keywords: card shuffling
Wikidata QID: Q101004836
author: L. Flatto
author: Andrew Odlyzko
author: David Wales
reviewed by: Ulrich Krengel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993073
OpenAlex ID: W2058006306
DOI: 10.1214/AOP/1176993073
description: scientific article; zbMATH DE number 3899830