ABSTRACT
Suppose A n $ A_n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math1_1.tif"/> is an n × n $ n\times n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math1_2.tif"/> matrix. Let λ 1 , … , λ n $ \lambda _1, \ldots , \lambda _n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math1_3.tif"/> denote its eigenvalues. When the eigenvalues are real, our convention will be to always write them in descending order. The empirical spectral measure μ n $ \mu _n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math1_4.tif"/> of A n $ A_n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/inline-math1_5.tif"/> is the measure given by μ n = 1 n ∑ i = 1 n δ λ i , $$ \begin{aligned} \mu _n= \frac{1}{n} \sum _{i=1}^n \delta _{ \lambda _i}, \end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429488436/725f3a92-cccc-4b3b-961a-84021a8d495e/content/math1_1.tif"/>
