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

One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…

We propose efficient random features for approximating a new and rich class of kernel functions that we refer to as Generalized Zonal Kernels (GZK). Our proposed GZK family, generalizes the zonal kernels (i.e., dot-product kernels on the…

This paper continues the study of a kernel family which uses the Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the exponential families theory. We extend the theory to cover generating measures with support that…

Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take…

We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…

A new differential equation is derived for an object ${\widehat S}(E,E^\prime,x)$, which when integrated over the appropriate range in $x$, yields the kernel $K(E,E^\prime)$ with which $n$-point correlation functions can be computed in a…

Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…

We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…

For a class of $O(n+1,R)$ invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the associated Bergman spaces, discuss the corresponding asymptotic expansions of…

We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, generalizing determinantal measures (which correspond to the case $k=2$). We give examples coming from the positive…

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…

This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a $(\mathbb{N}\times\mathbb{N})$-parameter family of fractals which are regarded as projective limits of metric measure…

A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main…

As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…

We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-N\Sigma_{i=1}^{N}V_{\alpha}(z_{i})}…

This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various…

Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation…

The family of Mat\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for…

This article considers Whittaker's function $W_{\kappa ,\mu }$ where $\kappa$ is real and $\mu$ is real or purely imaginary. Then $\varphi (x)=x^{-\mu -1/2}W_{\kappa ,\mu }(x)$ arises as the scattering function of a continuous time linear…

In this paper we analyze the covariance kernel of the Gaussian process that arises as the limit of fluctuations of linear spectral statistics for Wigner matrices with a few moments. More precisely, the process we study here corresponds to…