Probability Seminar
Date: March 26, 2018
Time: 2:00PM - 3:00PM
Location: BLOC 220
Speaker: Pierre Tarrago, CIMAT
Title: Subordination methods for free deconvolution
Abstract: The classical deconvolution of measures is an important problem which consists in recovering the distribution of a random variable from the knowledge of the random variable modified by an independent noise with known distribution. In this talk, I will discuss the free version of this problem: how can we recover the distribution of a non-commutative random variable from the knowledge of the distribution of the random variable modified by the addition (or multiplication) of a free independent noise? Since large independent random matrices in general positions are approximately free, an answer to the former question is a first step in the extraction of the spectral distribution of a large matrix from the knowledge of the matrix with an additive or multiplicative noise. Contrary to the classical case, the free convolution is not described by an integral kernel like the Fourier transform. This problem has been circumvented by Biane, Voiculescu, Belinschi and Bercovici which developed a fixed point method called subordination. I will explain how this method can be used to reduce the free deconvolution problem to a classical one. This is a joint work with Octavio Arizmendi (CIMAT) and Carlos Vargas (CIMAT).