Elliptic Extensions In Statistical And Stochastic Systems
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Elliptic Extensions In Statistical And Stochastic Systems
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Author : Makoto Katori
language : en
Publisher: Springer Nature
Release Date : 2023-04-06
Elliptic Extensions In Statistical And Stochastic Systems written by Makoto Katori and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-06 with Science categories.
Hermite's theorem makes it known that there are three levels of mathematical frames in which a simple addition formula is valid. They are rational, q-analogue, and elliptic-analogue. Based on the addition formula and associated mathematical structures, productive studies have been carried out in the process of q-extension of the rational (classical) formulas in enumerative combinatorics, theory of special functions, representation theory, study of integrable systems, and so on. Originating from the paper by Date, Jimbo, Kuniba, Miwa, and Okado on the exactly solvable statistical mechanics models using the theta function identities (1987), the formulas obtained at the q-level are now extended to the elliptic level in many research fields in mathematics and theoretical physics. In the present monograph, the recent progress of the elliptic extensions in the study of statistical and stochastic models in equilibrium and nonequilibrium statistical mechanics and probability theory is shown. At the elliptic level, many special functions are used, including Jacobi's theta functions, Weierstrass elliptic functions, Jacobi's elliptic functions, and others. This monograph is not intended to be a handbook of mathematical formulas of these elliptic functions, however. Thus, use is made only of the theta function of a complex-valued argument and a real-valued nome, which is a simplified version of the four kinds of Jacobi's theta functions. Then, the seven systems of orthogonal theta functions, written using a polynomial of the argument multiplied by a single theta function, or pairs of such functions, can be defined. They were introduced by Rosengren and Schlosser (2006), in association with the seven irreducible reduced affine root systems. Using Rosengren and Schlosser's theta functions, non-colliding Brownian bridges on a one-dimensional torus and an interval are discussed, along with determinantal point processes on a two-dimensional torus. Their scaling limits are argued, and the infinite particle systems are derived. Such limit transitions will be regarded as the mathematical realizations of the thermodynamic or hydrodynamic limits that are central subjects of statistical mechanics.
Local Fields And Their Extensions Second Edition
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Author : Ivan B. Fesenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-07-17
Local Fields And Their Extensions Second Edition written by Ivan B. Fesenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-17 with Mathematics categories.
This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor -groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's -class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor -groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas.
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Stochastic Processes And Applications
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Author : Grigorios A. Pavliotis
language : en
Publisher: Springer
Release Date : 2014-11-19
Stochastic Processes And Applications written by Grigorios A. Pavliotis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Library Of Congress Subject Headings
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Author : Library of Congress. Subject Cataloging Division
language : en
Publisher:
Release Date : 1980
Library Of Congress Subject Headings written by Library of Congress. Subject Cataloging Division and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Subject headings categories.
Library Of Congress Subject Headings
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Author : Library of Congress
language : en
Publisher:
Release Date : 1998
Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Subject headings categories.
Statistical Multiple Integration
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Author : Nancy Flournoy
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Statistical Multiple Integration written by Nancy Flournoy and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
High dimensional integration arises naturally in two major sub-fields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both. Recent advances in computational power have stimulated significant new advances in both Bayesian and classical multivariate statistics. In many statistical problems, however, multiple integration can be the major obstacle to solutions. This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Statistical Multiple Integration, held in June 1989 at Humboldt State University in Arcata, California. The conference represents an attempt to bring together mathematicians, statisticians, and computational scientists to focus on the many important problems in statistical multiple integration. The papers document the state of the art in this area with respect to problems in statistics, potential advances blocked by problems with multiple integration, and current work directed at expanding the capability to integrate over high dimensional surfaces.
Recent Advances In Computational Optimization
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Author : Stefka Fidanova
language : en
Publisher: Springer Nature
Release Date : 2025-03-03
Recent Advances In Computational Optimization written by Stefka Fidanova and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Computers categories.
This book presents recent advances in computational optimization. The book includes important real problems like modelling of physical processes, workforce planning problem, transportation problems, machine scheduling, air pollution modelling, optimization of fast-food restaurant chain, solving engineering, and financial problems. Our everyday life is unthinkable without optimization. We try to minimize our effort and maximize the achieved profit. Many real-world and industrial problems arising in engineering, economics, medicine, and other domains can be formulated as optimization tasks. The book is a comprehensive collection of extended contributions from the Workshops on Computational Optimization 2023. It shows how to develop algorithms for them based on new intelligent methods like evolutionary computations, ant colony optimization, constrain programming Monte Carlo method, and others. This research demonstrates how some real-world problems arising in engineering, economics, and other domains can be formulated as optimization problems.
Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics
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Author : Xerox University Microfilms
language : en
Publisher:
Release Date : 1973
Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics written by Xerox University Microfilms and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Dissertations, Academic categories.
Stanford Bulletin
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Author :
language : en
Publisher:
Release Date : 2004
Stanford Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.