Distribution of the shape of Markovian random words

• 成果类型: Article
• 署名作者: Chistyakov, GP; Götze, F
• 署名单位: National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0327-6
• 发表日期: 2004
• 页码: 18-36
• 关键词: longest increasing subsequences; Moderate Deviations; length

摘要

The distribution of the shape lambda 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 kxk 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.