Finite size effects. The averaged eigenvalue density of Wigner random sign real symmetric matrices
arXiv:1605.03562 · doi:10.1103/PhysRevE.93.062115
Abstract
Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known as highly relevant, in topics ranging from ferroelectrics to quotation networks. Combining these two points leads to examine finite size random matrices. To obtain basic materials properties, the Green function associated to the matrix has to be calculated. In order to obtain the first finite size correction a perturbative scheme is hereby developed within the framework of the replica method. The averaged eigenvalue spectrum and the corresponding Green function of Wigner random sign real symmetric N x N matrices to order 1/N are in fine obtained analytically. Related simulation results are also presented. The comparison between the analytical formulae and finite size matrices numerical diagonalization results exhibits an excellent agreement, confirming the correctness of the first order finite size expression.
arXiv comment11 pages; 8 figures; 71 references; prepared for Phys Rev E
References in corpus (19)
- Universal and non-universal properties of cross-correlations in financial time series
- Random-matrix theory of Majorana fermions and topological superconductors
- Random Matrix Theory Analysis of Cross Correlations in Financial Markets
- Orthogonal polynomial ensembles in probability theory
- Spectra of random graphs with arbitrary expected degrees
- Random graph models for directed acyclic networks
- Statistical mechanics of complex neural systems and high dimensional data
- Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
- Temporal correlations versus noise in the correlation matrix formalism: an example of the brain auditory response
- Coexistence of opposite opinions in a network with communities
- Finite size correction to the spectrum of regular random graphs: an analytical solution
- Spectra of sparse non-Hermitian random matrices: an analytical solution
- Localization of eigenvectors in random graphs
- Finite size corrections to disordered Ising models on Random Regular Graphs
- Asymmetric correlation matrices: an analysis of financial data
- Complex-valued information entropy measure for networks with directed links (digraphs). Application to citations by community agents with opposite opinions
- Organization of networks with tagged nodes and biased links: a priori distinct communities. The case of Intelligent Design Proponents and Darwinian Evolution Defenders
- A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros
- Particle diagrams and embedded many-body random matrix theory