A functional CLT for partial traces of random matrices

2018/03/06 by Jan Nagel, Nagel, Jan · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1803.02151

arxiv created 2019/07/19 · arxiv updated 2019/07/22

Abstract

In this paper we show a functional central limit theorem for the sum of the first \lfloor t n \rfloor diagonal elements of f(Z) as a function in t, for Z a random real symmetric or complex Hermitian n× n matrix. The result holds for orthogonal or unitarily invariant distributions of Z, in the cases when the linear eigenvalue statistic tr f(Z) satisfies a CLT. The limit process interpolates between the fluctuations of individual matrix elements as f(Z)_1,1 and of the linear eigenvalue statistic. It can also be seen as a functional CLT for processes of randomly weighted measures.

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