89 citations · 102 across the 2 of their papers we have counts for
6 papers
Littelmann paths and brownian paths
Philippe Biane, Philippe Bougerol, Neil O'Connell
We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.
Free probability and combinatorics
Philippe Biane
A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of…
Approximate factorization and concentration for characters of symmetric groups
Philippe Biane
We prove a factorization-concentration result for characters of symmetric groups. This is then applied to the asymptotic behaviour of the decomposition of the tensor representation…
A Free Probability Analogue of the Wasserstein Metric on the Trace-State Space
Philippe Biane, Dan Voiculescu
We define a free probability analogue of the Wasserstein metric, which extends the classical one. In dimension one, we prove that the square of the Wasserstein distance to the semi…
Computation of some examples of Brown's spectral measure in free probability
Philippe Biane, Franz Lehner
We use free probability techniques for computing spectra and Brown measures of some non hermitian operators in finite von Neumann algebras. Examples include u_n+u_oo where u_n and…
Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions
P. Biane, J. Pitman, M. Yor
This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular pr…