Monod, NicolasGheysens, Maxime2017-08-212017-08-212017-08-21201710.5075/epfl-thesis-7823https://infoscience.epfl.ch/handle/20.500.14299/139743urn:nbn:ch:bel-epfl-thesis7823-1We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups admit nonabelian free subgroups in that measure-theoretical sense. Consequences for affine actions and for unitarizability are then drawn. In particular, we obtain a new characterization of amenability via some affine actions on Hilbert spaces. Along the way, various fixed-point properties for groups are studied. We also give a survey of several useful facts about group representations on Banach spaces, continuity of group actions, compactness of convex hulls in locally convex spaces, and measurability pathologies in Banach spaces.enamenabilitygroup representationfixed-point propertyvon Neumann problemDixmier probleminduced representationtychomorphismKrein space.thesis::doctoral thesis