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Random walks on countable groups

Michael Björklund (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori)
Israel Journal of Mathematics (0021-2172). Vol. 217 (2017), 1, p. 371-382.
[Artikel, refereegranskad vetenskaplig]

We begin by giving a new proof of the equivalence between the Liouville property and vanishing of the drift for symmetric random walks with finite first moments on finitely generated groups; a result which was first established by Kaimanovich-Vershik and Karlsson-Ledrappier. We then proceed to prove that the product of the Poisson boundary of any countable measured group (G,mu) with any ergodic (G,mu)-space is still ergodic, which in particular yields a new proof of weak mixing for the double Poisson boundary of (G,mu) when mu is symmetric. Finally, we characterize the failure of weak-mixing for an ergodic (G,mu)-space as the existence of a non-trivial measure-preserving isometric factor.

Nyckelord: poisson boundary, Mathematics

Denna post skapades 2017-05-03. Senast ändrad 2017-07-03.
CPL Pubid: 249087


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Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)



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