Related papers: Hadwiger Integration of Random Fields

A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

This work develops, from a functional analytic perspective, the construction of random variables in Lebesgue spaces L^p. It extends classical notions of measurability, integrability, and expectation to L^p valued functions, using Pettis's…

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…

We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…

Gaussian processes are used in many machine learning applications that rely on uncertainty quantification. Recently, computational tools for working with these models in geometric settings, such as when inputs lie on a Riemannian manifold,…

We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced…

We establish formulas that give the intrinsic volumes, or curvature measures, of sublevel sets of functions defined on Riemannian manifolds as integrals of functionals of the function and its derivatives. For instance, in the Euclidean…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

We propose a new alternative gauge for the Einstein equations instead of the de Donder gauge, which allows in the limit of weak fields a straightforward integration of these equations. The Newtonian potential plays a new interesting role in…

The transverse coherence functions (TCFs) of phase and amplitude fluctuations of a seismic wave are powerful to estimate the spatial distribution, length scales, and strength of random heterogeneities. However, TCFs have been formulated for…

We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid, and apply it to the Bader charge partitioning for the electron charge density. Starting with the…

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…

Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…

We show a Dvoretsky-Rogers type Theorem for the adapted version of the $q$-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the…

We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…

In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness…

We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration…