Corpus ID: 235458550

# A Real-World Markov Chain arising in Recreational Volleyball

@inproceedings{Aldous2021ARM,
title={A Real-World Markov Chain arising in Recreational Volleyball},
author={D. Aldous and M. Cruz},
year={2021}
}
• Published 2021
• Mathematics
Card shuffling models have provided simple motivating examples for the mathematical theory of mixing times for Markov chains. As a complement, we introduce a more intricate realistic model of a certain observable real-world scheme for mixing human players onto teams. We quantify numerically the effectiveness of this mixing scheme over the 7 or 8 steps performed in practice. We give a combinatorial proof of the non-trivial fact that the chain is indeed irreducible.

#### References

SHOWING 1-10 OF 10 REFERENCES
Mixing times of lozenge tiling and card shuffling Markov chains
We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach itsExpand
Finite Markov Chains and Algorithmic Applications
1. Basics of probability theory 2. Markov chains 3. Computer simulation of Markov chains 4. Irreducible and aperiodic Markov chains 5. Stationary distributions 6. Reversible Markov chains 7. MarkovExpand
Understanding Markov Chains
This book provides an undergraduate introduction to discrete and continuoustime Markov chains and their applications. A large focus is placed on the first step analysis technique and its applicationsExpand
Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion
In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of cards. We prove that around time N^2\log N/(2\pi^2), the total-variation distance to equilibrium ofExpand
Markov chains and mixing times
For our purposes, a Markov chain is a (finite or countable) collection of states S and transition probabilities pij, where i, j ∈ S. We write P = [pij] for the matrix of transition probabilities.Expand
Trailing the Dovetail Shuffle to its Lair
• Mathematics
• 1992
We analyze the most commonly used method for shuffling cards. The main result is a simple expression for the chance of any arrangement after any number of shuffles. This is used to give sharp boundsExpand
Random walks on finite groups and rapidly mixing markov chains
© Springer-Verlag, Berlin Heidelberg New York, 1983, tous droits reserves. L’acces aux archives du seminaire de probabilites (Strasbourg) (http://www-irma. u-strasbg.fr/irma/semproba/index.shtml),Expand
Analysis of casino shelf shuffling machines
• Mathematics
• 2013
Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical adviceExpand
From shuffling cards to walking around the building: an introduction to modern Markov chain theory
• In Proceedings of the International Congress of Mathematicians, Vol. I (Berlin,
• 1998
Shuffling Cards, 7 Is Winning Number
• The New York Times, January
• 1990