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The main goal of the paper is to establish the existence of tensor product decompositions for those prime ideals P of the generic algebra A of quantum n by n matrices which are invariant under winding automorphisms of A. More specifically,…
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…
The purpose of this paper is to generalize this relation of symmetry between the power sum polynomials and the generalized Euler polynomials to the relation between the power sum polynomials and the generalized higher-order Euler…
The Matsumoto--Yor (MY) property of the generalized inverse Gaussian and gamma distributions has many generalizations. As it was observed in (Letac and Weso{\l}owski in Ann Probab 28:1371--1383, 2000) the natural framework for the…
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.
In this paper, we extend the previous convergence results for the generalized alternating projection method applied to subspaces in [arXiv:1703.10547] to hold also for smooth manifolds. We show that the algorithm locally behaves similarly…
Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…
A generalization of the generalized inverse Weibull distribution so-called transmuted generalized inverse Weibull dis- tribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a…
We address the recently introduced notions of generalized principal bundle and generalized principal connection by keeping track of global geometric properties through local coordinate transformation laws. This approach leads us to…
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…
Symmetry postulates play a crucial role in various approaches to reconstruct quantum theory from a few basic principles. Discrete and continuous symmetries are under consideration. The continuous case better matches the physical needs for…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…
The $Q$-prime curvature is a local pseudo-Einstein invariant on CR manifolds defined by Case and Yang, and Hirachi. Its integral, the total $Q$-prime curvature, gives a non-trivial global CR invariant. On the other hand, Marugame has…
This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently…
We study general transformation on the density matrix of two-level system that keeps the expectation value of observable invariant. We introduce a set of generators that yields hermiticity and trace preserving general transformation which…
Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…