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We give a new construction of tensor product gamma factors for a pair of irreducible representations of $\operatorname{GL}_c\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_k\left(\mathbb{F}_q\right)$. This construction is a finite field…

We study the existence and the properties of solutions to the Dirichlet problem for uniformly elliptic second-order Hamilton-Jacobi-Bellman operators, depending on the principal eigenvalues of the operator.

This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an $\alpha$-stable law, for $0<\alpha<1$, and the other variable has the law…

Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the introduction of the degenerate Bernoulli and degenerate Euler polynomials by Carlitz. The aim…

We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli random hopping probabilities. For the process mixed with these and continuous time dynamics, we obtain a single…

In this paper, we apply the combinatorial results on counting permutations with fixed pinnacle and vale sets to evaluate the special values of the spectral zeta functions of Sturm-Liouville differential operators. As applications, we get a…

Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type…

The probability density functions measured by Lewis and Swinney for turbulent Couette-Taylor flow, observed by Bodenschatz and co-workers in the Lagrangian measurement of particle accelerations and those obtained in the DNS by Gotoh et al.…

We find a recursive expression for the Bessel function of S. I. Gelfand for irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$. We show that special values of the Bessel function can be realized as the…

We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating…

Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are…

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the…

We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish…

Building upon the theory of graph limits and the Aldous-Hoover representation and inspired by Panchenko's work on asymptotic Gibbs measures (Annals of Probability 2013), we construct continuous embeddings of discrete probability…

We study the double Grothendieck polynomials of Kirillov--Naruse for the symplectic and odd orthogonal Grassmannians. These functions are explicitly written as sums of Pfaffian and are identified with the stable limits of the fundamental…

In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…

The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…

We introduce and study symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with $\Delta=\pm 1/2$. There is also a close relation to…

As properties of poly-Bernoulli numbers, a number of formulas such as the duality formula, explicit formula using the Stirling numbers of the second kind and periodicity for negative upper-index have been established. For the multi-indexed…

We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum double Schubert polynomial coincides with some quantum…