Related papers: Equivalent symmetric kernels of determinantal poin…

We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for…

We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix generalisation of the gamma process. We show that eigenvalues of…

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions…

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…

In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…

We show that the central limit theorem for linear statistics over determinantal point processes with $J$-Hermitian kernels holds under fairly general conditions. In particular, We establish Gaussian limit for linear statistics over…

Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…

The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalised to discrete settings involving either a linear or exponential lattice. The corresponding correlation functions can be expressed…

Consider $a$ particles performing simple, symmetric, non-intersecting random walks, starting at points $2(j-1)$, $1\le j\le a$ at time 0 and ending at $2(j-1)+c-b$ at time $b+c$. This can also be interpreted as a random rhombus tiling of an…

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…

For the exclusion process with symmetric kernel p(x,y)=p(y,x), the set of invariant measures has been completely studied. This paper gives results concerning the invariant measures for exclusion processes where p(x,y)=p(y,x) except for…

Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…

We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…

This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…

Product matrix processes are multi-level point processes formed by the singular values of random matrix products. In this paper we study such processes where the products of up to $m$ complex random matrices are no longer independent, by…

We define a determinantal point process on the complex projective space that reduces to the so-called spherical ensemble for complex dimension 1 under identification of the 2-sphere with the Riemann sphere. Through this determinantal point…

We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of…

The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data…

A unified approach is given to kernel functions which intertwine Ruijsenaars difference operators of type A and of type BC. As an application of the trigonometric cases, new explicit formulas for Koornwinder polynomials attached to single…

In this paper, we describe families of those bounded linear operators on a separable Hilbert space that are simultaneously unitarily equivalent to integral operators on $L_2(R)$ with bounded and arbitrarily smooth Carleman kernels. The main…