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Activity Number: 481 - Random Matrices and High-Dimensional Statistics
Type: Invited
Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #300224
Title: Large Random Matrices: Spiked Models, Stationnary Processes and Applications
Author(s): Jamal Najim*
Companies: CNRS and Université Paris-Est
Keywords: Large Covariance Matrices; Eigenvalues; Spiked Models; Stationnary observations; Central Limit Theorem

In this talk, we will review some of the classical models of large random matrices, namely large empirical covariance matrices, of interest in many applications such as statistics, electrical engineering and data science.

Given a population covariance matrix, the associated large empirical covariance matrix can exhibit a spectrum with many interesting features such as multiple connected components, outliers (that is lonely eigenvalues outside from the main bulk), etc. Much information about the underlying data structure can be gained from a precise analysis of the matrix eigenstructure.

We will review classical and modern results on spiked models and outliers, multiple connected component spectrum. We will then present recent results on samples of stationnary observations which substantially modify the classical landscape.

Talk based on joint papers with Banna, Hachem, Hardy, Merlevède, Tian

Authors who are presenting talks have a * after their name.

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