Distribution of the shape of Markovian random words

The distribution of the shape of the semi-standard tableau of a random word in k letters is asymptotically given by the distribution of the spectrum of a random traceless k k Gaussian Unitary Ensemble (GUE) matrix provided that these letters are independent with uniform distribution. Kuperberg (2002...

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Bibliographic Details
Published in:Probability theory and related fields 2004-05, Vol.129 (1), p.18-36
Main Authors: CHISTYAKOV, G. P, GÖTZE, F
Format: Article
Language:English
Subjects:
Alphabets
Codes
Combinatorics
Distribution theory
Exact sciences and technology
General topics
Inference from stochastic processes
time series analysis
Markov analysis
Markov chains
Mathematics
Probability
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Studies
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Summary:The distribution of the shape of the semi-standard tableau of a random word in k letters is asymptotically given by the distribution of the spectrum of a random traceless k k Gaussian Unitary Ensemble (GUE) matrix provided that these letters are independent with uniform distribution. Kuperberg (2002) conjectured that this result by Johansson (2001) remains valid if the letters of the word are generated by an irreducible Markov chain on the alphabet with cyclic transition matrix. In this paper we give a proof of this conjecture for an alphabet with k = 2 letters. [PUBLICATION ABSTRACT]
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-003-0327-6