Abstract
We establish a large deviation principle for the empirical spectral measure of a sample covariance matrix with sub-Gaussian entries, which extends Bordenave and Caputo’s result for Wigner matrices having the same type of entries [7]. To this aim, we need to establish an asymptotic freeness result for rectangular free convolution, more precisely, we give a bound in the subordination formula for information-plus-noise matrices.
Highlights
Throughout this paper, P(E) will denote the set of probability measures on a space E, Mn,p(R)
Let us first recall some basic facts in random matrix theory (RMT)
A key object in RMT is the empirical spectral measure of a matrix A ∈ Hn(C), namely the probability measure on R defined by μA
Summary
Throughout this paper, P(E) will denote the set of probability measures on a space E, Mn,p(R) Complex) matrices, Hn(C) the set of n × n Hermitian matrices, At Transconjugate) of a matrix A, and Tr(A) its trace. For a random variable X, Xdenotes the centred variable X − E(X). For two real numbers x, y, we denote by x ∧ y the minimum of x and y
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