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Hadwiger integrals employ the intrinsic volumes as measures for integration of real-valued functions. We provide a formula for the expected values of Hadwiger integrals of Gaussian-related random fields. The expected Hadwiger integrals of…
Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data…
This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics.…
Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…
We calculate Euclidean correlation functions through next-to-leading order in the low energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop…
We complete the two-loop calculation of beta-functions for vacuum expectation values (VEVs) in gauge theories by the missing O(g^4)-terms. The full two-loop results are presented for generic and supersymmetric theories up to two-loop level…
We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and…
In classical statistics, a well known paradigm consists in establishing asymptotic equivalence between an experiment of i.i.d. observations and a Gaussian shift experiment, with the aim of obtaining optimal estimators in the former…
We determine the fermion mass dependence of Euclidean finite volume partition functions for three-dimensional QCD in the epsilon-regime directly from the effective field theory of the pseudo-Goldstone modes by using zero-dimensional…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
Symmetry plays a fundamental role in the security analysis of quantum key distribution (QKD). Here we review how symmetry is exploited in continuous-variable (CV) QKD to prove the optimality of Gaussian attacks in the finite-size regime. We…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
The Gaussian wavefunctional approach is developed in thermofield dynamics. We manufacture thermal vacuum wavefunctional, its creation as well as annihilation operators,and accordingly thermo-particle excited states. For a (D+1)-dimensional…
Let $X_1,X_2, \ldots$ be independent and identically distributed random elements taking values in a separable Hilbert space $\mathbb{H}$. With applications for functional data in mind, $\mathbb{H}$ may be regarded as a space of…
We study the transport property of Gaussian measures on Sobolev spaces of periodic functions under the dynamics of the one-dimensional cubic fractional nonlinear Schr\"{o}dinger equation. For the case of second-order dispersion or greater,…
We theoretically propose and experimentally demonstrate a nonclassicality test of single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our…
The non-Gaussian operation can be used not only to enhance and distill the entanglement between Gaussian entangled states, but also to improve quantum communications. In this paper, we propose an non-Gaussian continuous-variable quantum key…