Concentration for noncommutative polynomials in random matrices
Mark W. Meckes, Stanislaw J. Szarek
TL;DR
This paper establishes a concentration inequality for linear functionals of noncommutative polynomials in various random matrix ensembles, providing a unified theoretical framework for understanding their fluctuations.
Contribution
It introduces a new concentration inequality applicable to a wide range of random matrix models involving noncommutative polynomials.
Findings
Applicable to Gaussian, bounded, unitary, and orthogonal matrices
Provides bounds for linear functionals of noncommutative polynomials
Unifies concentration results across different matrix ensembles
Abstract
We present a concentration inequality for linear functionals of noncommutative polynomials in random matrices. Our hypotheses cover most standard ensembles, including Gaussian matrices, matrices with independent uniformly bounded entries and unitary or orthogonal matrices.
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