Algebraically recurrent random walks on groups
Hilary Finucane (MIT)
Romain Tessera (ÉNS Lyon)
Abstract
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.
Full Text: Download PDF | View PDF online (requires PDF plugin)
Pages: 1-8
Publication Date: April 15, 2013
DOI: 10.1214/ECP.v18-2519
References
- Furstenberg, Harry. A Poisson formula for semi-simple Lie groups. Ann. of Math. (2) 77 1963 335--386. MR0146298
- Kaĭmanovich, 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. MR0931055
- Kaĭmanovich, V. A.; Vershik, A. M. Random walks on discrete groups: boundary and entropy. Ann. Probab. 11 (1983), no. 3, 457--490. MR0704539
- Khoshnevisan, Davar; Xiao, Yimin; Zhong, Yuquan. Local times of additive Lévy processes. Stochastic Process. Appl. 104 (2003), no. 2, 193--216. MR1961619
- Olʹšanskiĭ, 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. MR0586204

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