Related papers: Permanental random variables, ${M}$-matrices and $…
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
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 establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
In this paper, we give some determinantal and permanental representations of generalized bivariate Fibonacci p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
In this note we settle two open problems in the theory of permanents by using recent results from other areas of mathematics. Bapat conjectured that certain quotients of permanents, which generalize symmetric function means, are concave. We…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent…
In this paper, we consider a system of homogeneous algebraic equations in complex variables and their conjugates, which arise naturally from the range criterion for separability of PPT states. We examine systematically these equations to…
This paper is motivated by basic complexity and probability questions about permanents of random matrices over finite fields, and in particular, about properties separating the permanent and the determinant. Fix $q = p^m$ some power of an…
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…
We introduce a new kind of free independence, called real infinitesimal freeness. We show that independent orthogonally invariant with infinitesimal laws are asymptotically real infinitesimally free. We introduce new cumulants, called real…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.
We study in this paper the sufficient conditions for enhanced continuity of random fields, i.e. such that the modulus of its continuity allows the factorable representation by the product of random variable on the deterministic module of…
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…