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Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

Computation · Statistics 2024-02-02 Ahmad Farooq , Cristian A. Galvis-Florez , Simo Särkkä

A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…

General Mathematics · Mathematics 2015-04-29 Tokiniaina Ranaivoson , Raoelina Andriambololona , Rakotoson Hanitriarivo

Non-integer dimensions are commonplace in quantum field theories (QFTs) through dimensional regularization. In particular this affects angular calculations involving dot products. The structure of these rises from the generally accepted…

Mathematical Physics · Physics 2020-09-03 Juuso Österman

Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…

In the Gaussian-modulated coherent state quantum key distribution (QKD) protocol, the sender first generates Gaussian distributed random numbers and then encodes them on weak laser pulses actively by performing amplitude and phase…

Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…

Functional Analysis · Mathematics 2009-11-07 Estelle L. Basor

Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…

Numerical Analysis · Mathematics 2022-08-25 Peter Opsomer , Daan Huybrechs

Equivalence testing for scalar data has been well addressed in the literature, however, the same cannot be said for functional data. The resultant complexity from maintaining the functional structure of the data, rather than using a scalar…

Applications · Statistics 2015-03-05 Colin B. Fogarty , Dylan S. Small

The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic…

Statistical Mechanics · Physics 2011-11-08 Sanjib Sabhapandit

Generalized Parton Distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative…

High Energy Physics - Lattice · Physics 2025-11-25 Sebastian Grieninger , Jake Montgomery , Felix Ringer , Ismail Zahed

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and coworkers, we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions…

Materials Science · Physics 2021-08-20 Junjie Yang , Qi Ou , Zheng Pei , Hua Wang , Binbin Weng , Kieran Mullen , Yihan Shao

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…

Quantum Physics · Physics 2019-02-01 E M Graefe , B Longstaff , T Plastow , R Schubert

A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to…

Numerical Analysis · Mathematics 2024-10-10 Jonas A. Actor , Anthony Gruber , Eric C. Cyr , Nathaniel Trask

We apply the method of Hankel transforms to develop goodness-of-fit tests for gamma distributions with given shape parameter and unknown rate parameter, thereby extending results of Baringhaus and Taherizadeh (2010) on the exponential…

Statistics Theory · Mathematics 2018-10-17 Elena Hadjicosta , Donald Richards

This work explores displaced fermionic Gaussian operators with nonzero linear terms. We first demonstrate equivalence between several characterizations of displaced Gaussian states. We also provide an efficient classical simulation protocol…

Quantum Physics · Physics 2024-11-28 Xingjian Lyu , Kaifeng Bu

We develop a general framework for isotropic functional Gaussian fields on the $d$-dimensional sphere $\mathbb{S}^{d}$, where the field takes values in a separable Hilbert space $\mathcal{H}$. We establish an operator-valued extension of…

Statistics Theory · Mathematics 2025-12-01 Alessia Caponera , Vinicius Ferreira , Emilio Porcu

The quantum models of a massive scalar particle inside of an open bag generated by a pseudo-Gaussian conformaly flat (1+1) metrics are investigated. The potential of a free moving test particle, in the generated metric, has Gaussian…

Quantum Physics · Physics 2014-10-08 Felix Iacob

We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.

Probability · Mathematics 2012-08-13 Paweł J. Szabłowki

We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…

Quantum Physics · Physics 2008-09-12 Filippo Caruso , Vittorio Giovannetti

We study the regularity of the law of a quadratic form $Q(X,X)$, evaluated in a sequence $X = (X_{i})$ of independent and identically distributed random variables, when $X_{1}$ can be expressed as a sufficiently smooth function of a…

Probability · Mathematics 2024-06-21 Ronan Herry , Dominique Malicet , Guillaume Poly