University of Paris VI, France

We study a generalized version of the signaling processoriginally introduced and studied by Argiento, Pemantle, Skyrms and Volkov(2009), which models how two interacting agents learn to signal each other andthus create a common language.

We show that the process asymptotically leads to the emergence of a graph ofconnections between signals and states which has the property that nosignal-state correspondance could be associated both to a synonym and aninformational bottleneck.

A version of Lyons theory of rough path calculus which applies to a

subclass of rough paths for which more geometric interpretations are

valid will be presented. Application will be made to the Brownian and

to the (fractional) support theorem.