|TITLE:||Free probability and random matrices|
|SPEAKER:||Alice Guionnet (MIT)|
|DATE:||Vendredi, 1 Mars 2013|
Free probability is a theory initiated by D. Voiculescu in the eighties that studies non-commutative random variables. It is equipped with a notion of freeness, which is related with free products, and which plays the same role as independence in standard probability. Free probability is also a natural framework to study random matrices at the limit where their size goes to infinity. Conversely, random matrices provide natural tools and concepts in free probability. In this talk, we will introduce basic concepts in free probability and discuss its relation with random matrices. We will finally describe some uses of free probability theory in operator algebra.
About the speaker: Alice Guionnet is Professor of Mathematics at MIT as of 2012, from École Normale Supérieure (ENS) Lyon, where she served as a Director of Research CNRS. She received the MS from ENS Paris in 1993 and the PhD, under the guidance of G. Ben Arous at Université Paris Sud in 1995. Guionnet is a world leading probabilist, working on a program related to operator algebra theory and mathematical physics. She has made important contributions in random matrix theory, including large deviations, topological expansions, but also more classical study of their spectrum and eigenvectors. At ENS Lyon she built a top-ranking probability group, attracting and organizing top researchers. From 2006-2011 she served as Editor-in-Chief of Annales de L’Institut Henri Poincaré (currently on its editorial board), and also serves on the editorial board of Annals of Probability. She has given two Plenary talks and a number of Invited Talks at international meetings, including ICM. Her distinctions include the Miller Institute Fellowship, (2006), the Loève Prize (2009) and the Silver Medal of CNRS (2010).