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On reducibility and spectral properties of circulant Markov processes

Author

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  • Bolaños-Servin, Jorge R.
  • Carbone, Raffaella
  • Quezada, Roberto

Abstract

Motivated by applications in a wide variety of fields, we study the communication (or congruence) classes of a continuous time Markov walk on a circulant graph. This study is connected to some periodicity properties of the spectrum of the infinitesimal generator and has immediate consequences on the asymptotic behavior of the process. Some sharp bounds for the spectral gap are deduced.

Suggested Citation

  • Bolaños-Servin, Jorge R. & Carbone, Raffaella & Quezada, Roberto, 2017. "On reducibility and spectral properties of circulant Markov processes," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 27-33.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:27-33
    DOI: 10.1016/j.spl.2016.11.025
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    References listed on IDEAS

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    1. Gnacadja, Gilles, 2012. "Asymptotic equidistribution of congruence classes with respect to the convolution iterates of a probability vector," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1849-1852.
    2. Avrachenkov, Konstantin & Cottatellucci, Laura & Maggi, Lorenzo & Mao, Yong-Hua, 2013. "Maximum entropy mixing time of circulant Markov processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 768-773.
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