Related papers: Moment kernels, nested defects, and Cuntz dilation…
Given a contractive tuple of Hilbert space operators satisfying certain $A$-relations we show that there exists a unique minimal dilation to generators of Cuntz-Krieger algebras or its extension by compact operators. This Cuntz-Krieger…
A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown. The conditions under which the…
Discontinuity in density functions is of economic importance and interest. For instance, in studies on regression discontinuity designs, discontinuity in the density of a running variable suggests violation of the no-manipulation…
In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…
In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we…
In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…
We construct Euclidean random fields $X$ over $\R^d$, by convoluting generalized white noise $F$ with some integral kernels $G$, as $X=G* F$. We study properties of Schwinger (or moment) functions of $X$. In particular, we give a general…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
Consider $d$ commuting $C_{0}$-semigroups (or equivalently: $d$-parameter $C_{0}$-semigroups) over a Hilbert space for $d \in \mathbb{N}$. In the literature (\textit{cf.} [29, 26, 27, 23, 18, 25]), conditions are provided to classify the…
We discuss a variety of developments in the study of large time behavior of the positive minimal heat kernel of a time independent (not necessarily symmetric) second-order parabolic operator defined on a domain M in $R^d$, or more…
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…
Cumulant oscillations, or $H_q$ moment oscillations, appear if the KNO multiparticle distribution decreases at large z, $z\equiv n/ <n>$, faster than the exponential, $exp(-D z^\mu)$, with $\mu > 1$. In nucleus-nucleus interactions this…
We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…
We derive a consistency result, in the $L_1$-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order $p(\geq 1)$, we obtain…
We study the weak convergence of iterates of so-called centred kernel quadratic stochastic operators. These iterations, in a population evolution setting, describe the additive perturbation of the arithmetic mean of the traits of an…
This paper describes the mechanism of defect-mediated relaxation in a dodecagonal square-triangle random tiling phase exhibited by a simulated binary mixture of soft discs in 2D. We examine the internal transitions within the elementary…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…