A rule of thumb for riffle shuffling

DOI10.1214/10-AAP701zbMath1226.60005arXiv0908.3462WikidataQ56095224 ScholiaQ56095224MaRDI QIDQ549858

Sami Assaf, Persi Diaconis, Kannan Soundararajan

Publication date: 19 July 2011

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.3462

zbMATH Keywords

card shufflingGilbert-Shannon-Reeds model for riffle shuffling

Mathematics Subject Classification ID

Combinatorial probability (60C05) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items

Shuffling cards by spatial motion, Analysis of casino shelf shuffling machines, Hopf algebras and Markov chains: two examples and a theory, An exercise(?) in Fourier analysis on the Heisenberg group, Functions of random walks on hyperplane arrangements, Cutoff for the Bernoulli-Laplace urn model with \(o(n)\) swaps, On the joint distribution of descents and signs of permutations, Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement, Carries, shuffling, and symmetric functions, Lumpings of algebraic Markov chains arise from subquotients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Total variation cutoff in birth-and-death chains
• Functions of random walks on hyperplane arrangements
• Strong uniform times and finite random walks
• Trailing the dovetail shuffle to its lair
• No-feedback card guessing for dovetail shuffles
• Riffle shuffles, cycles, and descents
• Random walks on trees and matchings
• Applications of symmetric functions to cycle and increasing subsequence structure after shuffles
• A card shuffling analysis of deformations of the Plancherel measure of the symmetric group
• Riffle shuffles and their associated dynamical systems
• The \(L^{2}\)-cutoff for reversible Markov processes
• Riffle shuffles of decks with repeated cards
• Normal approximations for descents and inversions of permutations of multisets
• Carries, Shuffling, and an Amazing Matrix
• Projections of probability distributions
• The cutoff phenomenon for randomized riffle shuffles
• Shuffling Cards and Stopping Times
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• Generating a random permutation with random transpositions
• Carries, Combinatorics, and an Amazing Matrix
• On Choosing and Bounding Probability Metrics
• Symmetry Analysis of Reversible Markov Chains