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We attempt to solve the Einstein equations for string dust and null flowing radiation for the general axially symmetric metric, which we believe is being done for the first time. We obtain the string-dust and radiating generalizations of…

General Relativity and Quantum Cosmology · Physics 2008-02-03 L. K. Patel , N. Dadhich , A. Beesham

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…

Methodology · Statistics 2019-04-10 Victor M. Panaretos , Yoav Zemel

This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the…

High Energy Physics - Theory · Physics 2009-10-29 Robbert Dijkgraaf , Domenico Orlando , Susanne Reffert

Stein's method allows to prove distributional convergence of a sequence of random variables and to quantify it with respect to a given metric such as Kolmogorov's (a Berry-Ess\'een type theorem). Mod-* convergence quantifies the convergence…

Probability · Mathematics 2017-01-12 Yacine Barhoumi-Andréani

We present a theory of quantum work statistics in generic chaotic, disordered Fermi liquid systems within a driven random matrix formalism. By extending P. W. Anderson's orthogonality determinant formula to compute quantum work…

Mesoscale and Nanoscale Physics · Physics 2023-03-16 András Grabarits , Márton Kormos , Izabella Lovas , Gergely Zaránd

This study introduces the CIR3 model, a three-factor model characterized by stochastic and correlated trends and volatilities. The paper focuses on establishing the Wasserstein ergodicity of this model, a task not achievable through…

Probability · Mathematics 2024-04-09 Giacomo Ascione , Michele Bufalo , Giuseppe Orlando

The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…

Statistics Theory · Mathematics 2023-09-26 Peter J. Forrester

We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…

Probability · Mathematics 2018-02-28 Nicolas Privault , Grzegorz Serafin

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…

Probability · Mathematics 2024-11-08 Fraser Daly

We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the…

Probability · Mathematics 2021-12-13 Yingdong Lu

In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein…

Functional Analysis · Mathematics 2024-11-19 Erlan D. Nursultanov , Durvudkhan Suragan

The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that…

Computational Physics · Physics 2024-12-16 Xiaoxu Li , Huajie Chen

We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de…

Probability · Mathematics 2013-08-20 Ivan Nourdin , Giovanni Peccati , Yvik Swan

We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…

Probability · Mathematics 2019-04-08 Benjamin Arras , Christian Houdré

We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma…

Probability · Mathematics 2016-06-28 Erol A. Peköz , Adrian Röllin , Nathan Ross

Let $(X_{i}, i\in J)$ be a family of locally dependent nonnegative integer-valued random variables, and consider the sum $W=\sum\nolimits_{i\in J}X_i$. We first establish a general error upper bound for $d_{TV}(W, M)$ using Stein's method,…

Probability · Mathematics 2023-12-12 Zhonggen Su , Vladimir V. Ulyanov , Xiaolin Wang

We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by…

Probability · Mathematics 2008-02-07 Adrian Röllin

We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size--bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily…

Probability · Mathematics 2020-07-07 A. D. Barbour , Nathan Ross , Yuting Wen

We use Stein's method to obtain a bound on the distance between scaled $p$-dimensional random walks and a $p$-dimensional (correlated) Brownian Motion. We consider dependence schemes including those in which the summands in scaled sums are…

Probability · Mathematics 2020-06-09 Mikołaj J. Kasprzak

We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central…

Probability · Mathematics 2025-02-19 Christian Döbler