Random matrix ensembles with column/row constraints: part I

TL;DR

This paper investigates how specific row and column sum constraints in complex matrices influence their spectral properties, revealing new correlations, localization effects, and a novel universality class bridging Poisson and Gaussian orthogonal ensembles.

Contribution

It introduces a new class of constrained random matrix ensembles and analyzes their spectral statistics, uncovering unique correlations and a new universality class.

Findings

Constraints induce correlations among eigenfunctions.

Constraints hinder eigenfunction delocalization.

Spectral statistics reveal a new universality class.

Abstract

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new correlations among eigenfunctions, hinders their complete delocalization and affects the eigenvalues too. Our results reveal a rich behavior hidden beneath the spectral statistics and also indicate the presence of a new universality class analogous to that of a Brownian ensemble appearing between Poisson and Gaussian orthogonal ensemble.