Free probability for probabilists

This is an introduction to some of the most probabilistic aspects of free probability theory

On the formula of Goulden and Rattan for Kerov polynomials

We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.Comment: 4 page

Concavification of free entropy

We introduce a modification of Voiculescu's free entropy which coincides with the liminf variant of Voiculescu's free entropy on extremal states, but is a concave upper semi-continuous function on the trace state space. We also extend the orbital free entropy of Hiai, Miyamoto and Ueda to non-hyperfinite multivariables and prove freeness in case of additivity of Voiculescu's entropy (or vanishing of our extended orbital entropy).Comment: 28 pages, final version : details added in several proofs and relations to other variants of free entropy explaine

Littelmann paths and brownian paths

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.Comment: 30 pages, 1 figur