Related papers: A Generalization of Random Matrix Ensemble II: Con…
Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…
We give a method for computing the ensemble average of multiplicative class functions over the Gaussian ensemble of real asymmetric matrices. These averages are expressed in terms of the Pfaffian of Gram-like antisymmetric matrices formed…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…
In complex systems such as spin systems and protein systems, conventional simulations in the canonical ensemble will get trapped in states of energy local minima. We employ the generalized-ensemble algorithms in order to overcome this…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…
In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…
We investigate $\beta$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium…
We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…
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…
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…
Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…
We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with…
We consider the moment space $\mathcal{M}_n$ corresponding to $p \times p$ real or complex matrix measures defined on the interval $[0,1]$. The asymptotic properties of the first $k$ components of a uniformly distributed vector $(S_{1,n},…
We solve a family of Gaussian two-matrix models with rectangular Nx(N+v) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter mu. Our model can be thought of as the chiral extension of the real…
The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting…