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Asymptotics and spectral results for random walks on p-adics

Author

Listed:
  • Albeverio, Sergio
  • Karwowski, Witold
  • Zhao, Xuelei

Abstract

Markov semigroups on the field of p-adic numbers which are symmetric with respect to a measure [rho](x) dx absolutely continuous relative to the Haar measure dx on are constructed. The corresponding Dirichlet forms and associated Markov processes are exhibited and shown to be of the jump type. A detailed description of the spectrum of the generator (eigenvalues and eigenfunctions) is provided. Necessary and sufficient conditions for reducibility, recurrence and transience are found. Results about exit times from balls are also presented, as well as a proof of null recurrence.

Suggested Citation

  • Albeverio, Sergio & Karwowski, Witold & Zhao, Xuelei, 1999. "Asymptotics and spectral results for random walks on p-adics," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 39-59, September.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:1:p:39-59
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    References listed on IDEAS

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    1. 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. Kaneko, Hiroshi, 2000. "A class of spatially inhomogeneous Dirichlet spaces on the p-adic number field," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 161-174, July.
    2. D. A. Dawson & L. G. Gorostiza, 2018. "Transience and Recurrence of Random Walks on Percolation Clusters in an Ultrametric Space," Journal of Theoretical Probability, Springer, vol. 31(1), pages 494-526, March.
    3. Hiroshi Kaneko & Xuelei Zhao, 2006. "Transition Semi–groups on a Local Field Induced by Galois Group and their Representation," Journal of Theoretical Probability, Springer, vol. 19(1), pages 221-234, January.

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