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- W2077092485 abstract "Let G be a real algebraic semi-simple group, X an isometric extension of the flag space of G by a compact group C. We assume that G is topologically transitive on X. We consider a closed sub-semigroup T of G and a probability measure μ on T such that T is Zariski-dense in G and the support of μ generates T. We show that there is a finite number of T-invariant minimal subsets in X and these minimal subsets are the supports of the extremal μ-stationary measures on X. We describe the structure of these measures, we show the conditional equidistribution on C of the μ-random walk and we calculate the algebraic hull of the corresponding cocycle. A certain subgroup generated by the “spectrum” of T can be calculated and plays an essential role in the proofs. Soient G un groupe semi-simple algébrique réel, X une extension isométrique de l'espace des drapeaux de G par un groupe compact. Nous supposons que G est topologiquement transitif sur X. Nous considérons un sous-semi-groupe fermé T de G, Zariski-dense, et une mesure de probabilité μ sur T adaptée à T. Nous montrons que l'ensemble des fermés T-invariants minimaux de X est fini et que ces fermés minimaux sont les supports des mesures de probabilités μ-stationnaires extrémales. Nous décrivons la structure de ces probabilités, nous montrons l'équidistribution conditionnelle de la marche aléatoire de loi μ et nous déterminons l'enveloppe algébrique du cocycle associé. Un certain sous-groupe engendré par le « spectre » de T est calculé et joue un rôle essentiel dans les démonstrations." @default.
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- W2077092485 date "2007-03-01" @default.
- W2077092485 modified "2023-10-18" @default.
- W2077092485 title "Actions of large semigroups and random walks on isometric extensions of boundaries" @default.
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- W2077092485 doi "https://doi.org/10.1016/j.ansens.2007.01.003" @default.
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