Related papers: Noncommutative Christoffel-Darboux Kernels
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…
The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…
By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The…
This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multi-dimensional central limit…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. We here unveil an analogy with…
We revisit the problem of computing extremal and non-extremal three point functions of semiclassical probes with single trace operators and point out certain inconsistencies in previous approaches in the literature. We clarify the roles of…
In previous works, the second author defined directional Robin constants associated to a compact, nonpolar subset $K$ of an algebraic curve $A$ in $\mathbb{C}^N$ and related these to a natural class of Chebyshev constants for $K$. We define…
It is the purpose of this article to outline a course that can be given to engineers looking for an understandable mathematical description of the foundations of distribution theory and the necessary functional analytic methods. Arguably,…
For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the…
In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random…
Symmetric kernel matrices are a well-researched topic in the literature of kernel based approximation. In particular stability properties in terms of lower bounds on the smallest eigenvalue of such symmetric kernel matrices are thoroughly…
Using Laurent expansions of the Kontsevich-Vishik canonical trace of holomorphic families of classical pseudodifferential operators, we define functionals on the space of Riemannian metrics and investigate their conformal properties,…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…
This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin wave model, or width fluctuations of a two dimensional Edwards-Wilkinson…
Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
We introduce mollified Christoffel-Darboux (CD) kernels on varieties, a systematic regularization of the classical CD kernel associated with a probability measure on a compact domain. The main motivations are twofold: first, to sharpen the…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…