Enumerative Theory for the Tsetlin Library

2023/06/28 by Chatterjee, Sourav, Diaconis, Persi, Kim, Gene B. · 1 citation
#60B15 #60J99 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.16521

Abstract

The Tsetlin library is a well-studied Markov chain on the symmetric group S_n. It has stationary distribution π(σ) the Luce model, a nonuniform distribution on S_n, which appears in psychology, horse race betting, and tournament poker. Simple enumerative questions, such as ``what is the distribution of the top k cards?'' or ``what is the distribution of the bottom k cards?'' are long open. We settle these questions and draw attention to a host of parallel questions on the extension to the chambers of a hyperplane arrangement.

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• Permuton and local limits for the Luce model

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