Orateur
Gaëtan Borot
Description
I will describe a theory of free cumulants to all orders (g,n), both
at the level of combinatorics (surfaced permutations) and generating
series (higher R-transform machinery). Freeness up to order (g,n) is
then defined by the additivity of free cumulants up to order (g,n).
(0,1) is the usual freeness, (1/2,1) is infinitesimal freeness, (0,n)
is the n-order freeness of Collins-Mingo-Speicher-Sniady. This theory
is adapted to address all-order (in particular, beyond leading order)
asymptotic expansions in unitarily invariant ensembles of random
hermitian matrices. I will discuss its application to GUE +
deterministic.
