相关论文: Finite range Decomposition of Gaussian Processes

The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of…

Let G(x,y) and G_D(x,y) be the Green functions of rotationally invariant symmetric \alpha-stable process in R^d and in an open set D respectively, where 0<\alpha < 2. The inequality G_D(x,y)G_D(y,z)/G_D(x,z) \le c(G(x,y)+G(y,z)) is a very…

We determine the decomposition of V_{\sqrt{2}D_l} into a sum of irreducible T-modules for general l where D_l is the root lattice of type D_l and T is the tensor product of l+1 Virasoro vertex operator algebras with central charges…

The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb…

We investigate the use of renormalisation group methods to solve partial differential equations (PDEs) numerically. Our approach focuses on coarse-graining the underlying continuum process as opposed to the conventional numerical analysis…

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…

It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is…

In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master L\'evy measure and the associated L\'evy-It\^o…

This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…

This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this goal, the paper develops new geometric and analytical…

We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance…

We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in $3 \leq d\leq 6$ Euclidean…

A combination of continuum and lattice methods is used to investigate systematic issues in the finite-energy-sum-rule determination of $V_{us}$ based on flavor-breaking combinations of hadronic $\tau$ decay data. Results for $V_{us}$…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

For a one-parameter family of simple metrics of constant curvature ($4\kappa$ for $\kappa\in (-1,1)$) on the unit disk $M$, we first make explicit the Pestov-Uhlmann range characterization of the geodesic X-ray transform, by constructing a…

We introduce and analyze a nonlocal generalization of Whittle--Mat\'ern Gaussian fields in which the smoothness parameter varies in space through the fractional order, $s=s(x)\in[\underline{s}\,,\bar{s}]\subset(0,1)$. The model is defined…

Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…

As is known, a process of form $\int_0^t\eta_sd\langle B\rangle_s-\int_0^t2G(\eta_s)ds$, $\eta\in M^1_G(0,T)$, is a non-increasing $G$-martingale. In this paper, we shall show that a non-increasing $G$-martingale could not be form of…

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…

Let $A \subset \mathbb{R}$ be finite. We quantitatively improve the Balog-Wooley decomposition, that is $A$ can be partitioned into sets $B$ and $C$ such that $$\max\{E^+(B) , E^{\times}(C)\} \lesssim |A|^{3 - 7/26}, \ \ \max \{E^+(B,A) ,…