Sum rules and large deviations for spectral matrix measures
Probability
2016-09-21 v2 Classical Analysis and ODEs
Abstract
A sum rule relative to a reference measure on R is a relationship between the reversed Kullback-Leibler divergence of a positive measure on R and some non-linear functional built on spectral elements related to this measure (see for example Killip and Simon 2003). In this paper, using only probabilistic tools of large deviations, we extend the sum rules obtained in Gamboa, Nagel and Rouault (2015) to the case of Hermitian matrix-valued measures. We recover the earlier result of Damanik, Killip and Simon (2010) when the reference measure is the (matrix-valued) semicircle law and obtain a new sum rule when the reference measure is the (matrix-valued) Marchenko-Pastur law.
Keywords
Cite
@article{arxiv.1601.08135,
title = {Sum rules and large deviations for spectral matrix measures},
author = {Fabrice Gamboa and Jan Nagel and Alain Rouault},
journal= {arXiv preprint arXiv:1601.08135},
year = {2016}
}