Random matrix ensembles with column/row constraints. II

TL;DR

This paper numerically investigates real-symmetric random matrix ensembles with column and row constraints, revealing complex spectral behaviors and confirming analytical predictions about their fluctuations resembling a critical Brownian ensemble.

Contribution

It extends previous work by numerically analyzing spectral statistics of constrained ensembles under various conditions, confirming their critical fluctuation behavior.

Findings

Spectral statistics show rich, complex behavior.

Results confirm analytical predictions about spectral fluctuations.

Spectral fluctuations resemble a critical Brownian ensemble.

Abstract

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath the spectral statistics and also confirm our analytical predictions, presented in part I of this paper, about the analogy of their spectral fluctuations with those of a critical Brownian ensemble which appears between Poisson and Gaussian orthogonal ensemble.