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The geometry of triples of antipodal ideal chambers of affine buildings
Corina Ciobotaru, Corentin Le Bars
In this article, we investigate two notions of genericity for triples of antipodal ideal chambers in a locally finite affine building : one defined at the ideal boundary $X^{\in…
Dynamical boundaries of affine buildings: C*-simplicity and Poisson boundaries
Corina Ciobotaru, Corentin Le Bars
We investigate a class of groups acting on possibly exotic affine buildings and possessing good proximal properties. Such groups are termed of general type, and their dynamics…
A Tits alternative for -buildings of type
Corentin Le Bars, Jean Lécureux, Jeroen Schillewaert
Let be a group with a non-elementary action on a (not necessarily discrete) -buildings. We prove that, given a random walk on , isometries in are strongly r…
Stationary measures and random walks on -buildings
Corentin Le Bars
We consider a non-elementary group action of a locally compact second countable group on a possibly exotic non-discrete affine building of type $\til…
Random walks and rank one isometries on CAT(0) spaces
Corentin Le Bars
Let be a discrete group, a measure on and a proper CAT(0) space. We show that if acts non-elementarily with a rank one element on , then the pushforward $\{Z…