Random matrix ensembles with column/row constraints: part I

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.

The old version is now divided into parts with numerical results given in Random matrix ensembles with column/row constraints: part II, submitted as a new arXiv

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• Eigenfunction statistics of Laguerre Brownian ensemble
• Statistical analysis of chiral structured ensembles: role of matrix constraints
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Extended states with Poisson spectral statistics
• Spectral and Strength Statistics of Chiral Brownian Ensemble
• Patterned Random Matrices: deviations from universality
• Statistics of the non-zero eigenvalues and singular values of low-rank random matrices with non-negative entries
• A class of 2x2 correlated random-matrix models with Brody spacing distribution