Convergence of spherical averages for actions of free groups

By Alexander I. Bufetov. 2002

60 citations recorded by the source corpus.

Let (X, v) be a probability space and suppose a free group Fm with m generators acts on (X, v) by measure-preserving transformations. Let {ai,..., am} be a set of free generators for Fm and let T1,..., Tm: X --* X be transformations corresponding to the generators. Write T-i = T-1 for i = 1,..., m, and set A = {-m,...,-1, 1,..., m}. We also have the action Fm on L1 (X, v), defined by Tg(p o Tg-1, g E Fm. Consider the set WA of all finite words over the alphabet A:

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ead2ae0ff5e2a027ffa3518a389ca5130be57d0a

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Citations in the corpus

Mesures stationnaires et fermés invariants des espaces homogènes (2011, background): “2 est basée sur un argument de dérive exponentielle, reposant sur une adapatation des idées de [3] pour la démonstration de théorèmes ergodiques pour les actions de groupes libres.”
On ergodic theorems for free group actions on noncommutative spaces (2004, methodology): “Bufetov has proposed in [ 7 ] a totally different proof of the Nevo-Stein theorem.”