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A random walk on the profinite completion of Z

Author

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  • Cruz-López, Manuel
  • Estala-Arias, Samuel
  • Murillo-Salas, Antonio

Abstract

In this note we describe a continuous time random walk on the profinite completion Ẑ of the integers Z, which is a profinite group. The infinitesimal generator of the process is also discussed.

Suggested Citation

  • Cruz-López, Manuel & Estala-Arias, Samuel & Murillo-Salas, Antonio, 2016. "A random walk on the profinite completion of Z," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 130-138.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:130-138
    DOI: 10.1016/j.spl.2015.11.015
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    References listed on IDEAS

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    1. Urban, Roman, 2012. "Markov processes on the adeles and Dedekind’s zeta function," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1583-1589.
    2. Yasuda, Kumi, 2013. "Markov processes on the adeles and Chebyshev function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 238-244.
    3. Albeverio, Sergio & Karwowski, Witold, 1994. "A random walk on p-adics--the generator and its spectrum," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 1-22, September.
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    Cited by:

    1. Cruz-López, Manuel & Estala-Arias, Samuel, 2018. "A random walk on the profinite completion of a finitely generated group," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 7-16.

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