The Gaussian Approximation Potential PDF Download
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Author | : Albert Bartók-Pártay |
Publisher | : Springer Science & Business Media |
Total Pages | : 96 |
Release | : 2010-07-27 |
Genre | : Science |
ISBN | : 364214067X |
Download The Gaussian Approximation Potential Book in PDF, ePub and Kindle
Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited. The framework of Gaussian Approximation Potentials that is developed in this thesis allows us to generate interatomic potentials automatically, based on quantum mechanical data. The resulting potentials offer several orders of magnitude faster computations, while maintaining quantum mechanical accuracy. The method has already been successfully applied for semiconductors and metals.
Author | : |
Publisher | : |
Total Pages | : 104 |
Release | : 2011-07-11 |
Genre | : |
ISBN | : 9783642140686 |
Download The Gaussian Approximation Potential Book in PDF, ePub and Kindle
Author | : David Craig Morgan |
Publisher | : |
Total Pages | : 108 |
Release | : 1987 |
Genre | : Gaussian processes |
ISBN | : |
Download A Gaussian Approximation to the Effective Potential Book in PDF, ePub and Kindle
Author | : Florence Merlevède |
Publisher | : Oxford University Press, USA |
Total Pages | : 496 |
Release | : 2019-02-28 |
Genre | : Mathematics |
ISBN | : 9780198826941 |
Download Functional Gaussian Approximation for Dependent Structures Book in PDF, ePub and Kindle
Functional Gaussian Approximation for Dependent Structures to develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.
Author | : Sergey Bobkov |
Publisher | : Springer Nature |
Total Pages | : 438 |
Release | : 2023-06-18 |
Genre | : Mathematics |
ISBN | : 3031311493 |
Download Concentration and Gaussian Approximation for Randomized Sums Book in PDF, ePub and Kindle
This book describes extensions of Sudakov's classical result on the concentration of measure phenomenon for weighted sums of dependent random variables. The central topics of the book are weighted sums of random variables and the concentration of their distributions around Gaussian laws. The analysis takes place within the broader context of concentration of measure for functions on high-dimensional spheres. Starting from the usual concentration of Lipschitz functions around their limiting mean, the authors proceed to derive concentration around limiting affine or polynomial functions, aiming towards a theory of higher order concentration based on functional inequalities of log-Sobolev and Poincaré type. These results make it possible to derive concentration of higher order for weighted sums of classes of dependent variables. While the first part of the book discusses the basic notions and results from probability and analysis which are needed for the remainder of the book, the latter parts provide a thorough exposition of concentration, analysis on the sphere, higher order normal approximation and classes of weighted sums of dependent random variables with and without symmetries.
Author | : M. P. Pato |
Publisher | : |
Total Pages | : 0 |
Release | : |
Genre | : |
ISBN | : |
Download A COMPARISON OF THE GAUSSIAN APPROXIMATION AND LANGEVIN'S SIMULATION IN DIC. Book in PDF, ePub and Kindle
Author | : R. E. Walkup |
Publisher | : |
Total Pages | : 30 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download A Local Gaussian Approximation for the Propagation of a Classical Distribution Function Book in PDF, ePub and Kindle
Author | : Victor Chernozhukov |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Download Gaussian Approximation of Suprema of Empirical Processes Book in PDF, ePub and Kindle
This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove an abstract approximation theorem applicable to a wide variety of statistical problems, such as construction of uniform confidence bands for functions. Notably, the bound in the main approximation theorem is nonasymptotic and the theorem does not require uniform boundedness of the class of functions. The proof of the approximation theorem builds on a new coupling inequality for maxima of sums of random vectors, the proof of which depends on an e.ective use of Stein's method for normal approximation, and some new empirical process techniques. We study applications of this approximation theorem to local and series empirical processes arising in nonparametric estimation via kernel and series methods, where the classes of functions change with the sample size and are non-Donsker. Importantly, our new technique is able to prove the Gaussian approximation for the supremum type statistics under weak regularity conditions, especially concerning the bandwidth and the number of series functions, in those examples.
Author | : E. Mammen |
Publisher | : |
Total Pages | : 0 |
Release | : 1985 |
Genre | : |
ISBN | : |
Download Local Optimal Gaussian Approximation of an Exponential Family Book in PDF, ePub and Kindle
Author | : Dieter Landers |
Publisher | : |
Total Pages | : 22 |
Release | : 1976 |
Genre | : |
ISBN | : |
Download On Nonuniform Gaussian Approximation for Random Summation Book in PDF, ePub and Kindle