[seminarioDeProbabilidad] Seminario de Probabilidad y Procesos Estocásticos

[María Clara Fittipaldi]

Miércoles 6 de Noviembre las 13h15,
Salón S-104
Departamento de Matemáticas

Camille Male <http://camillemale.com/>
Institut de Mathématiques de Bordeaux

Nos hablará sobre "Asymptotic freeness over the diagonal of large random
matrices".

Abstract:
I will discuss the problem of computing the eigenvalues distribution of
polynomials in random matrices, in the limit where the size of the matrices
goes to infinity. In this context, Voiculescu's Free Probability Theory
gives analytic tools to consider this question when the random matrices are
in "generic position", in particular when they are invariant by conjugation
by unitary matrices. Here we work under a much weaker assumption, assuming
only that the random matrices are invariant in law by conjugation by
permutation matrices. This requires a more general method, known as Traffic
Probability Theory. Since recently, with this approach we were only able to
give a combinatorial description for the moments of the limit eigenvalues
distribution. More recently, we discovered that freeness in the sense of
traffics implies Voiculescu's notion of freeness with amalgamation over the
diagonal. In particular, this yields new numerical methods to compute
limiting eigenvalues distributions.

Organizan
Manuel Domínguez de la Iglesia
María Clara Fittipaldi
Arno Siri-Jégousse

Página web:
http://www.matem.unam.mx/~seminarioproba/

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