Stationary Distribution and Eigenvalues for a de Bruijn Process

Arvind Ayyer () and Volker Strehl ()
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Arvind Ayyer: University of California, Department of Mathematics
Volker Strehl: Universität Erlangen-Nürnberg, Department of Computer Science

A chapter in Advances in Combinatorics, 2013, pp 101-120 from Springer

Abstract: Abstract We define a de Bruijn process with parameters n and L as a certain continuous-time Markov chain on the de Bruijn graph with words of length L over an n-letter alphabet as vertices. We determine explicitly its steady state distribution and its characteristic polynomial, which turns out to decompose into linear factors. In addition, we examine the stationary state of two specializations in detail. In the first one, the de Bruijn-Bernoulli process, this is a product measure. In the second one, the Skin-deep de Bruin process, the distribution has constant density but nontrivial correlation functions. The two point correlation function is determined using generating function techniques.

Keywords: Correlation Function; Markov Chain; Stationary Distribution; Characteristic Polynomial; Product Measure (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-30979-3_5

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DOI: 10.1007/978-3-642-30979-3_5

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