Electronic Communications in Probability

Algebraically recurrent random walks on groups

Itai Benjamini, Hilary Finucane, and Romain Tessera

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Initial steps are presented towards understanding which finitely generated groups are almost surely generated as a semigroup by the path of a random walk on the group.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 28, 8 pp.

Accepted: 15 April 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C81: Random walks on graphs

random walks on groups recurrence/transience semi-group

This work is licensed under a Creative Commons Attribution 3.0 License.


Benjamini, Itai; Finucane, Hilary; Tessera, Romain. Algebraically recurrent random walks on groups. Electron. Commun. Probab. 18 (2013), paper no. 28, 8 pp. doi:10.1214/ECP.v18-2519. https://projecteuclid.org/euclid.ecp/1465315567

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  • Furstenberg, Harry. A Poisson formula for semi-simple Lie groups. Ann. of Math. (2) 77 1963 335–386.
  • KaÄ­manovich, V. A. Boundaries of random walks on polycyclic groups and the law of large numbers for solvable Lie groups. (Russian) Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1987, vyp. 4, 93–95, 112.
  • KaÄ­manovich, V. A.; Vershik, A. M. Random walks on discrete groups: boundary and entropy. Ann. Probab. 11 (1983), no. 3, 457–490.
  • Khoshnevisan, Davar; Xiao, Yimin; Zhong, Yuquan. Local times of additive Lévy processes. Stochastic Process. Appl. 104 (2003), no. 2, 193–216.
  • OlʹšanskiÄ­, A. Ju. On the question of the existence of an invariant mean on a group. (Russian) Uspekhi Mat. Nauk 35 (1980), no. 4(214), 199–200.