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Stationary Distribution and Eigenvalues for a de Bruijn Process

In: Advances in Combinatorics

Author

Listed:
  • Arvind Ayyer

    (University of California, Department of Mathematics)

  • Volker Strehl

    (Universität Erlangen-Nürnberg, Department of Computer Science)

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.

Suggested Citation

  • Arvind Ayyer & Volker Strehl, 2013. "Stationary Distribution and Eigenvalues for a de Bruijn Process," Springer Books, in: Ilias S. Kotsireas & Eugene V. Zima (ed.), Advances in Combinatorics, edition 127, pages 101-120, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-30979-3_5
    DOI: 10.1007/978-3-642-30979-3_5
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