Related papers: A System of Multivariable Krawtchouk Polynomials a…
Leveraging skew Howe duality, we show that Lawson-Lipshitz-Sarkar's spectrification of Khovanov's arc algebra gives rise to 2-representations of categorified quantum groups over $\mathbb{F}_2$ that we call spectral 2-representations. These…
This paper studies new Lancaster characterizations of bivariate multivariate Poisson, negative binomial and normal distributions which have diagonal expansions in multivariate orthogonal polynomials. The characterizations extend classical…
Uvarov-type perturbations for mixed-type multiple orthogonal polynomials on the step line are investigated within a matrix-analytic framework. The transformations considered involve both rational and additive modifications of a rectangular…
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of…
A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval $(0,1)$ is studied. This type of polynomials have direct applications in…
Recent years have seen substantial advances in the development of biofunctional materials using synthetic polymers. The growing problem of elusive sequence-functionality relations for most biomaterials has driven researchers to seek more…
We study Markov chains generated by iterated Lipschitz functions systems with possibly place dependent probabilities. Under general conditions, we prove uniqueness of the invariant probability measure for the associated Markov chain, by…
Some differential implications of classical Marx-Strohh\"acker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential…
An algebraic interpretation of the one-variable quantum $q$-Krawtchouk polynomials is provided in the framework of the Schwinger realization of $\mathcal{U}_{q}(sl_{2})$ involving two independent $q$-oscillators. The polynomials are shown…
We prove a variety of results describing the possible diagonals of tuples of commuting hermitian operators in type $II_1$ factors. These results are generalisations of the classical Schur-Horn theorem to the infinite dimensional,…
Markov processes are widely used models for investigating kinetic networks. Here we collate and present a variety of results pertaining to kinetic network models, in a unified framework. The aim is to lay out explicit links between several…
A review on spectral and differential-geometric properties of Delsarte transmutation operators in multidimension is given. Their differential geometrical and topological structure in multidimension is analyzed, the relationships with De…
We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the…
The paper is devoted to the study of configuration space analysis by using the projective spectral theorem. For a manifold $X$, let $\Gamma_X$, resp.\ $\Gamma_{X,0}$ denote the space of all, resp. finite configurations in $X$. The so-called…
The relationship between a stable multivariable polynomial $p(z)$ and the Fourier coefficients of its spectral density function $1/|p(z)|^2$, is further investigated. In this paper we focus on the radial asymptotics of the Fourier…
We discuss the relation between knot polynomials and the KP hierarchy. Mainly, we study the scaling 1-hook property of the coloured Alexander polynomial: $\mathcal{A}^\mathcal{K}_R(q)=\mathcal{A}^\mathcal{K}_{[1]}(q^{\vert R\vert})$ for all…
We introduce the notion of a $k$-mode weakly stationary quantum process $\varrho$ based on the canonical Schr\"odinger pairs of position and momentum observables in copies of $L^2(\mathbb{R}^k)$, indexed by an additive abelian group $D$ of…
Estimating the joint probability mass function (PMF) of a set of random variables lies at the heart of statistical learning and signal processing. Without structural assumptions, such as modeling the variables as a Markov chain, tree, or…
Hermitean Clifford analysis is a higher dimensional function theory centered around the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean conjugate complex Dirac operators. As an essential step towards the…
The Perron-Frobenius theorem plays an important role in many areas of management science and operations research. This paper provides a probabilistic perspective on the theorem, by discussing a proof that exploits a probabilistic…