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Texas A&M University
Mathematics

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).