相关论文: A hierarchy of Palm measures for determinantal poi…

We consider the problem of computation of the correlation functions for the z-measures with the deformation (Jack) parameters 2 or 1/2. Such measures on partitions are originated from the representation theory of the infinite symmetric…

We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…

Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems abd determines the…

Let $\pi_{\alpha}$ be a holomorphic discrete series representation of a connected semi-simple Lie group $G$ with finite center, acting on a weighted Bergman space $A^2_{\alpha} (\Omega)$ on a bounded symmetric domain $\Omega$, of formal…

Christoffel deformation of a measure on the real line consists of multipying this measure by a squared polynomial having its roots in $\R$. We introduce Christoffel deformations of discrete orthogonal polynomial ensembles by considering the…

Given a nontrivial positive measure $\mu$ on the unit circle, the associated Christoffel-Darboux kernels are $K_n(z, w;\mu) = \sum_{k=0}^{n}\overline{\varphi_{k}(w;\mu)}\,\varphi_{k}(z;\mu)$, $n \geq 0$, where $\varphi_{k}(\cdot; \mu)$ are…

We prove some estimations of the correlation of two local observables in quantum spin systems (with Schr\"odinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice,…

The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process -- a probability measure on a space of countable point configurations. The kernel is expressed…

We study Palm measures of determinantal point processes with $J$-Hermitian correlation kernels. A point process $\mathbb{P}$ on the punctured real line $\mathbb{R}^* = \mathbb{R}_{+} \sqcup \mathbb{R}_{-}$ is said to be $\textit{balanced…

This paper studies kernel Radon-Nikodym derivatives for the one-step shift of time-indexed positive definite kernels associated with random matrix products. The problem is to determine when the shifted kernel is dominated by the original…

Inspired by the covering-space method in path integral on multiply connected spaces, we here present a universal formula of time-evolution kernels for continuous- and discrete-time quantum walks on orbit spaces. In this note, we focus on…

We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two…

An effective formula for the Bergman kernel on $\mathbb{H}_{\gamma} = \{|z_1|^\gamma < |z_2| < 1 \}$ is obtained for rational $\gamma = \frac{m}{n} >1$. The formula depends on arithmetic properties of $\gamma$, which uncovers new symmetries…

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…

We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels…

We study Fredholm determinants related to a family of kernels which describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher order analogues of the Airy kernel and are…

We compute the full off-diagonal asymptotics of the equivariant and partial Bergman kernels associated with a circle action on a prequantized K\"ahler manifold with bounded geometry at infinity, then use these results to compute the…

We construct and analyze conformally invariant random fields on 4-dimensional Riemannian manifolds $(M,g)$. These centered Gaussian fields $h$, called \emph{co-biharmonic Gaussian fields}, are characterized by their covariance kernels $k$…

We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal…

We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of…