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A note on the Screaming Toes game

Part of: Combinatorial probability Combinatorics, graph theory, probability theory, statistics Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  17 January 2022

Simon Tavaré Open the ORCID record for Simon Tavaré [Opens in a new window]
Simon Tavaré*
Affiliation:
Columbia University
*
*Postal address: Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY 10027, USA. Email address: [email protected]
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Abstract

We investigate properties of random mappings whose core is composed of derangements as opposed to permutations. Such mappings arise as the natural framework for studying the Screaming Toes game described, for example, by Peter Cameron. This mapping differs from the classical case primarily in the behaviour of the small components, and a number of explicit results are provided to illustrate these differences.

Keywords

Random mappingderangementPoisson approximationPoisson–Dirichlet distributionprobabilistic combinatoricssimulationcomponent sizecycle size

MSC classification

Primary: 60C05: Combinatorial probability 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 65C05: Monte Carlo methods
Secondary: 97K20: Combinatorics 97K60: Distributions and stochastic processes 65C40: Computational Markov chains
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 1 , March 2022 , pp. 118 - 130
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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