Proprietes Asymptotiques des Relations d'Equivalences Mesurees Discretes
1999, v.5, №2, 163-200
We study the asymptotic properties of orbits of a measurable action on a probability space of a finitely generated group. We prove that if the measure in ergodic, stationary and non-invariant, then almost every orbit is transient. We prove that if the measure is stationary, then almost every orbit has 0,1,2 or a Cantor set of ends, and that almost every orbit with two ends has linear growth.
Keywords: measurable group actions,measured equivalence relations,ends,growth,randomwalks