Related papers: Permanental random variables, ${M}$-matrices and $…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
Previously, the graph permanent was introduced as a single-valued invariant for graphs $G$ with $|E(G)| = k(|V(G)|-1)$ for some $k \in \mathbb{Z}_{>0}$. Herein, we construct the extended graph permanent, an infinite sequence for all graphs.…
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…
We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
A t by n random matrix A is formed by sampling n independent random column vectors, each containing t components. The random Gram matrix of size n, G_n, contains the dot products between all pairs of column vectors in the randomly generated…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…
The principal result is a primary decomposition of ideals generated by the (2x2)-subpermanents of a generic matrix. These permanental ideals almost always have embedded components and their minimal primes are of three distinct heights. Thus…
We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued…
Computations involving invariant random vectors are directly related to the theory of invariants (cf. e.g \cite{Weing_1}). Some simple observations along these lines are presented in this paper. We note in particular that sum of elements of…
We present families of single determinantal representations of on-shell scalar products of Bethe vectors. Our families of representations are parameterized by a continuous complex variable which can be fixed at convenience. Here we consider…
The "2-variable general-$\lambda$-matrix polynomials (2VG$\lambda$MP)" is a new family of matrix polynomials, introduced and studied in this article. These matrix polynomials are constructed using umbral and symbolic methods. We delve into…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
Let $\Gamma$ be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of $\Gamma$ and proved them irreducible as representation of…
Computing the permanent of a non-negative matrix is a computationally challenging, \#P-complete problem with wide-ranging applications. We introduce a novel permanental analogue of Schur's determinant formula, leveraging a newly defined…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it…
We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distributed entries and $\Sigma$ is a $n \times n$ deterministic…