Un théorème de Choquet-Deny pour les groupes moyennables

Fonctions harmoniques positives sur certains groupes de Lie résolubles connexes

“…Cette construction généralise celle de [23] qui se limitait aux fonctions bi-cr-harmoniques. Pour les rudiments concernant la théorie des martingales et les chaînes de Markov nous renvoyons le lecteur non averti à [20] et [25].…”

Poisson boundary of groups acting on real trees

“…Discrete subgroups of SL(d, R) are treated in [27] where the Poisson boundary is related to the space of flags. For random walks on Lie groups, the study and the description of the Poisson boundary started in [25] and was extensively developed in the 70's and the 80's by many authors including Furstenberg [27,28], Azencott [3], Raugi and Guivarc'h [61,38,62], Ledrappier [49,5]. Some analogies between discrete groups and their continuous counterparts are enlightened, see [27,49,5], but some contrast can appear, compare [62] with [39,41].…”

“…For random walks on Lie groups, the study and the description of the Poisson boundary started in [25] and was extensively developed in the 70's and the 80's by many authors including Furstenberg [27,28], Azencott [3], Raugi and Guivarc'h [61,38,62], Ledrappier [49,5]. Some analogies between discrete groups and their continuous counterparts are enlightened, see [27,49,5], but some contrast can appear, compare [62] with [39,41]. The Poisson boundary of some Fuchsian groups has also been described by Series as being the limit set of the group [64].…”