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Concentration of Measure and Large Random Matrices with an application to Sample Covariance Matrices

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Abstract

The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory for random vectors. By providing various notions of vector concentration (q-exponential, linear, Lipschitz, convex), a set of elementary tools is laid out that allows for the immediate extension of classical results from random matrix theory involving random concentrated vectors in place of vectors with independent entries. These findings are exemplified here in the context of sample covariance matrices but find a large range of applications in statistical learning and beyond, starting with the capacity to easily analyze the performance of artificial neural networks and random feature maps.
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Dates and versions

hal-02020287 , version 1 (15-02-2019)

Identifiers

  • HAL Id : hal-02020287 , version 1

Cite

Cosme Louart, Romain Couillet. Concentration of Measure and Large Random Matrices with an application to Sample Covariance Matrices. 2019. ⟨hal-02020287⟩
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