Supersymmetry and Trace Formulae, Igor V. Lerner; Jonathan P. Keating; David E. Khme

Автор: A. N Borodin и P. Salminen
Название: Handbook of Brownian motion: facts and formulae
ISBN: 3034894627 ISBN-13(EAN): 9783034894623
Издательство: Springer
Цена: 18167.00 р.
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Описание: There are two parts in this book. The first part is devoted mainly to the proper- ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re- lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style." By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.

Автор: Jochen Br?ning; Victor W Guillemin; Shlomo Sternbe
Название: Supersymmetry and Equivariant de Rham Theory
ISBN: 3642084338 ISBN-13(EAN): 9783642084331
Издательство: Springer
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Цена: 14673.00 р.
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Описание: Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Bruning and V.W. Guillemin. The point of departure are two relatively short but very remarkable papers be Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie." These papers are reproduced here, together with a modern introduction to the subject, written by two of the leading experts in the field. This "introduction" comes as a textbook of its own, though, presenting the first full treatment of equivariant cohomology in the de Rahm setting. The well known topological approach is linked with the differential form aspect through the equivariant de Rahm theorem. The systematic use of supersymmetry simplifies considerably the ensuing development of the basic technical tools which are then applied to a variety of subjects, leading up to the localization theorems and other very recent results.

Автор: Grosche Christian
Название: Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae
ISBN: 9814460079 ISBN-13(EAN): 9789814460071
Издательство: World Scientific Publishing
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Цена: 19800.00 р.
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Описание: In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition.In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.

Автор: Pierre Del Moral
Название: Feynman-Kac Formulae
ISBN: 1441919023 ISBN-13(EAN): 9781441919021
Издательство: Springer
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Цена: 18167.00 р.
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Описание: The central theme of this book concerns Feynman-Kac path distributions, interacting particle systems, and genealogical tree based models. This re- cent theory has been stimulated from different directions including biology, physics, probability, and statistics, as well as from many branches in engi- neering science, such as signal processing, telecommunications, and network analysis. Over the last decade, this subject has matured in ways that make it more complete and beautiful to learn and to use. The objective of this book is to provide a detailed and self-contained discussion on these connec- tions and the different aspects of this subject. Although particle methods and Feynman-Kac models owe their origins to physics and statistical me- chanics, particularly to the kinetic theory of fluid and gases, this book can be read without any specific knowledge in these fields. I have tried to make this book accessible for senior undergraduate students having some familiarity with the theory of stochastic processes to advanced postgradu- ate students as well as researchers and engineers in mathematics, statistics, physics, biology and engineering. I have also tried to give an "expose" of the modem mathematical theory that is useful for the analysis of the asymptotic behavior of Feynman-Kac and particle models.