相关论文: Revisiting two strong approximation results of Dud…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

We study tail probabilities via some Gaussian approximations. Our results make refinements to large deviation theory. The proof builds on classical results by Bahadur and Rao. Binomial distributions and their tail probabilities are…

Recently, Chernozhukov, Chetverikov, and Kato [Ann. Statist. 42 (2014) 1564--1597] developed a new Gaussian comparison inequality for approximating the suprema of empirical processes. This paper exploits this technique to devise sharp…

We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.

We show how to formulate the phenomenon of gaugino condensation in a super-Yang-Mills theory with a field-dependent gauge coupling described with a linear multiplet. We prove the duality equivalence of this approach with the more familiar…

A possibility of strong coupling quantum Liouville gravity is investigated via infinite dimensional representations of $\qslc$ with $q$ at a root of unity. It is explicitly shown that vertex operator in this model can be written by a tensor…

Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…

Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by…

The strength of an extension of Kruskal's Theorem to certain pairs of cohabitation trees is calibrated.

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field…

This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…

In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these…

Two dimensional $N=\infty$ lattice chiral models are investigate by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic…

We study the evolution of the mass autocorrelation function by describing the growth of density fluctuations through the Zel'dovich approximation. The results are directly compared with the predictions of the scaling hypothesis for…

We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…

We study the properties of a family of distances between functions of a single variable. These distances are examples of integral probability metrics, and have been used previously for comparing probability measures on the line; special…

We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft and Witting (Z. Wahrsch. Verw. Gebiete 7 (1967) 289--302), where…

We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) we will use this to couple two…

We present a simple reform for treating the reported problem of loss-of-accuracy near the real axis of Humlicek's w4 algorithm, widely used for the calculation of the Faddeyeva or complex probability function. The reformed routine maintains…

We consider summability methods generated by the class GM(2b). We generalize some related results of P. Pych-Taberska [Studia Math. XCVI (1990), 91-103] on strong approximation of almost periodic functions by their Fourier series and S. M.…