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We introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic…
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution…
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
In this paper, we explore a ring invariant which is closely related to the Davenport constant of a group. In particular, we will calculate this invariant for a certain class of rings of integers and their orders and use it to understand…
Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated…
So far, the pseudo cross-variogram is primarily used as a tool for the structural analysis of multivariate random fields. Mainly applying recent theoretical results on the pseudo cross-variogram, we use it as a cornerstone in the…
We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we…
We develop kernel criteria for the likelihood-ratio, hazard-rate, usual stochastic, and relative log-concavity orders in parametric families of univariate probability laws with densities. The score is the derivative of the log density with…
This paper studies variance functions of Cauchy-Stieltjes Kernel families generated by compactly supported centered probability measures. We describe several operations that allow us to construct additional variance functions from known…
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
A two-level atom interacting with an electromagnetic mode in a cavity experiences population collapses and revivals. They are an indirect signature of the field quantization, and also hold information about the mode. Thus, they may be…
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained,…
Since the seminal work of Keating and Snaith, the characteristic polynomial of a random Haar-distributed unitary matrix has seen several of its functional studied or turned into a conjecture; for instance: $ \bullet $ its value in $1$…
For a family of near banded Toeplitz matrices, generalized characteristic polynomials are shown to be orthogonal polynomials of two variables, which include the Chebyshev polynomials of the second kind on the deltoid as a special case.…
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for…
We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined graded algebra. This construction generalizes to categorification of some special functions, such as Chebyshev polynomials.…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…