Related papers: A Generalization of Random Matrix Ensemble II: Con…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
We give an overview of the recursive characterisations of random matrix ensembles that are currently at the forefront of random matrix theory by way of studying two classes of ensembles using two different types of recursive schemes:…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components. Due to their broad expressive power, Gaussian mixture models…
A new method involving particle diagrams is introduced and developed into a rigorous framework for carrying out embedded random matrix calculations. Using particle diagrams and the attendant methodology including loop counting it becomes…
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such…
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
A polynomial ensemble is a probability density function for the position of $n$ real particles of the form $\frac{1}{Z_n} \, \prod_{j<k} (x_k-x_j) \, \det \left[ f_k (x_j) \right]_{j,k=1}^n$, for certain functions $f_1, \ldots, f_n$. Such…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
Using the Generalized Maximium Entropy Principle based on the nonextensive q entropy a new family of random matrix ensembles is generated. This family unifies previous extensions of Random Matrix Theory and gives rise to an orthogonal…
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…
We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of…
We study a class of random matrices arising from the Lax matrix structure of classical integrable systems, particularly the Calogero family of models. Our focus is the density of eigenvalues for these random matrices. The problem can be…
Embedded random matrix ensembles with $k$-body interactions are well established to be appropriate for many quantum systems. For these ensemble the two point correlation function is not yet derived though these ensembles are introduced 50…