Brazilian Journal of Probability and Statistics

A recurrent random walk on the $p$-adic integers

M. Cruz-López and A. Murillo-Salas

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This paper describes a random walk on the $p$-adic integers, which turns out to be recurrent.

Article information

Braz. J. Probab. Stat., Volume 30, Number 1 (2016), 145-154.

Received: October 2013
Accepted: September 2014
First available in Project Euclid: 19 January 2016

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Random walks $p$-adic integers


Cruz-López, M.; Murillo-Salas, A. A recurrent random walk on the $p$-adic integers. Braz. J. Probab. Stat. 30 (2016), no. 1, 145--154. doi:10.1214/14-BJPS265.

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  • Albeverio, S. and Karwowski, W. (1994). A random walk on $p$-adics—The generator and its spectrum. Stochastic Process. Appl. 53, 1–22.
  • Dudley, R. M. (1962). Random walks on abelian groups. Proc. Amer. Math. Soc. 13, 447–450.
  • Dragovich, B. and Dragovich, A. Yu. (2009). A $p$-adic model of DNA sequence and genetic code. $p$-Adic Numbers Ultrametric Anal. Appl. 1, 34–41.
  • Evans, S. N. (1989). Local properties of Lévy processes on a totally disconnected group. J. Theoret. Probab. 2, 209–259.
  • Koblitz, N. (1984). $p$-Adic Numbers, $p$-Adic Analysis, and Zeta-Functions, 2nd ed. Graduate Texts in Mathematics 58. New York: Springer.
  • Lukierska-Walasek, K. and Topolski, K. (2006). $p$-adic description of hierarchical systems dynamics. In $p$-Adic Mathematical Physics. AIP Conf. Proc. 826, 81–90. Melville, NY: Amer. Inst. Phys.
  • Robert, A. M. (2000). A Course in $p$-Adic Analysis. Graduate Texts in Mathematics 198. New York: Springer.
  • Wilson, J. S. (1998). Profinite Groups. London Mathematical Society Monographs. New Series 19. New York: The Clarendon Press, Oxford Univ. Press.