Related papers: Spectral fluctuations of multiparametric complex m…
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the…
We introduce a generalized ensemble of nonhermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an…
We study the spectral properties of a multiparametric system having particle-hole symmetry in random matrix setting. We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a…
We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…
We study the asymptotic spectral behavior of high-dimensional random Gram matrices with sparsity and a variance profile, motivated by applications in wireless communications. Specifically, we consider the Gram matrices $\mathbf S_n=\mathbf…
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…
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…
Multi-parametric chiral random matrix ensembles are important tools to analyze the statistical behavior of generic complex systems with chiral symmetry. A recent study \cite{psmulti} of the former maps them to the chiral Brownian ensemble…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number N(Q) of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
We present long range statistical properties of a recently introduced unitary random matrix ensemble, whose short range correlations were found to describe a transition from Wigner to Poisson type as a function of a single parameter.
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics when chaotic, or 2-dimensional (2d) Poisson statistics when integrable. We investigate the spectral properties of a…