Related papers: A Generalization of Random Matrix Ensemble I: Gene…
We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful…
Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products 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…
We provide a simple analytic relation which connects the density operator of the radiation field with the number probabilities. The problem of experimentally "sampling" a general matrix elements is studied, and the deleterious effects of…
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two…
The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings \beta = 1,2 and 4. It has been known for some time that there is an…
Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose…
We generalize the results on the asymptotic expansion from Gaussian Unitary Ensembles case to all Gaussian Ensembles. We derive differential equations on densities and their moment generating functions for all Gaussian Ensembles. Also, we…
The averages of ratios of characteristic polynomials det(lambda - X) of N x N random matrices X, are investigated in the large N limit for the GUE, GOE and GSE ensemble. The density of states and the two-point correlation function are…
We calculate the exact density of states (DOS) for the three classical and two non-classical Random Matrix Ensembles for finite matrix size N using supersymmetric integrals. The 1/N-Expansion yields already in lowest order good…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the $q$-lattice setting is considered. We take up the task of initiating a systematic study of the corresponding moments of the density from two…
Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…
In this work we find a new formula for matrix averages over the Gaussian ensemble. Let ${\bf H}$ be an $n\times n$ Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a-priori flat measure in the force phase space under the constraints…