Asymptotic Expansion Of A Partition Function Related To The Sinh Model

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Asymptotic Expansion Of A Partition Function Related To The Sinh Model

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Author : Gaëtan Borot
language : en
Publisher: Springer
Release Date : 2016-12-08

Asymptotic Expansion Of A Partition Function Related To The Sinh Model written by Gaëtan Borot and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Science categories.

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.

Asymptotics Of Random Matrices And Related Models The Uses Of Dyson Schwinger Equations

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Author : Alice Guionnet
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-29

Asymptotics Of Random Matrices And Related Models The Uses Of Dyson Schwinger Equations written by Alice Guionnet 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 2019-04-29 with Mathematics categories.

Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models. These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.

Issues In Applied Mathematics 2011 Edition

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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09

Issues In Applied Mathematics 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Mathematics categories.

Issues in Applied Mathematics / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Applied Mathematics. The editors have built Issues in Applied Mathematics: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Mathematics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Random Matrices And The Six Vertex Model

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Author : Pavel Bleher
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-04

Random Matrices And The Six Vertex Model written by Pavel Bleher 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 2013-12-04 with Mathematics categories.

This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric. Titles in this series are co-published with the Centre de Recherches Mathématiques.

Magnetic Properties Of Layered Transition Metal Compounds

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Author : L.J. de Jongh
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Magnetic Properties Of Layered Transition Metal Compounds written by L.J. de Jongh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

In the last two decades low-dimensional (low-d) physics has matured into a major branch of science. Quite generally we may define a system with restricted dimensionality d as an object that is infinite only in one or two spatial directions (d = 1 and 2). Such a definition comprises isolated single chains or layers, but also fibres and thin layers (films) of varying but finite thickness. Clearly, a multitude of physical phenomena, notably in solid state physics, fall into these categories. As examples, we may mention: • Magnetic chains or layers (thin-film technology). • Metallic films (homogeneous or heterogeneous, crystalline, amorphous or microcristalline, etc.). • I-d or 2-d conductors and superconductors. • Intercalated systems. • 2-d electron gases (electrons on helium, semiconductor interfaces). • Surface layer problems (2-d melting of monolayers of noble gases on a substrate, surface problems in general). • Superfluid films of ~He or 'He. • Polymer physics. • Organic and inorganic chain conductors, superionic conductors. • I-d or 2-d molecular crystals and liquid crystals. • I-d or 2-d ferro- and antiferro electrics.

Journal Of Physics A Mathematical And General

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Author : INSTITUTE OF PHYSICS. (Great Britain). AMERICAN INSTITUTE OF PHYSICS. (USA)
language : en
Publisher:
Release Date : 2002

Journal Of Physics A Mathematical And General written by INSTITUTE OF PHYSICS. (Great Britain). AMERICAN INSTITUTE OF PHYSICS. (USA) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematical physics categories.

Vector Partitions Visible Points And Ramanujan Functions

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Author : Geoffrey B. Campbell
language : en
Publisher: CRC Press
Release Date : 2024-05-29

Vector Partitions Visible Points And Ramanujan Functions written by Geoffrey B. Campbell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-29 with Mathematics categories.

Vector Partitions, Visible Points and Ramanujan Functions offers a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number theory and computational mathematics. It takes the reader up to research level, presenting new results alongside known classical results from integer partitions and areas of vector and multipartite partition theory. It also sets forth new directions for research for the more advanced reader. Above all, the intention of the book is to bring new inspiration to others who study mathematics and related areas. It is hoped that some new ideas will be launched to add value and insight into many of the classical and new theories surrounding partitions. The book is an appreciation of the many gifted authors of research into partitions over the past century and before, in the hope that more may come of this for future generations. Features Provides a step-by-step guide through the known literature on Integer and Vector Partitions, and a focus on the not so well-known Visible Point Vector identities Serves as a reference for graduate students and researchers in physics, applied mathematics, number theory and computational mathematics Offers a variety of practical examples as well as sets of exercises suitable for students and researchers Geoffrey B. Campbell completed his PhD at Australian National University in 1998 under the esteemed physicist Professor Rodney Baxter. His affiliation with the Australian National University Mathematical Sciences Institute has continued for over 30 years. Within that time frame, Geoffrey also served eight years as an Honorary Research Fellow at LaTrobe University Mathematics and Statistics Department in Melbourne. Currently he writes ongoing articles for the Australian Mathematical Society Gazette. Within the international scope, Geoffrey currently serves as a PhD external committee member for a mathematics graduate student at Washington State University in America. Geoffrey has built a career within Australian Commonwealth and State government departments, including as an Advisor at the Department of Prime Minister and Cabinet; as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.

Advances In Chemical Physics Volume 112

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Author : Ilya Prigogine
language : en
Publisher: John Wiley & Sons
Release Date : 2009-09-09

Advances In Chemical Physics Volume 112 written by Ilya Prigogine and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-09 with Science categories.

Dieser neueste Band setzt die Tradition der erfolgreichen, vielfach bewährten Reihe fort. Aus erster Hand erhält der Leser die aktuellsten Informationen über Fortschritte auf dem Gebiet der chemischen Physik. Ein hochkarätiges Forum der kritischen, kompetenten Diskussion! (05/00)

Exact Methods In Low Dimensional Statistical Physics And Quantum Computing

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Author : Jesper Jacobsen
language : en
Publisher: OUP Oxford
Release Date : 2010-04-22

Exact Methods In Low Dimensional Statistical Physics And Quantum Computing written by Jesper Jacobsen and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Science categories.

Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics.

Magnetic Excitations And Fluctuations Ii

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Author : Umberto Balucani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Magnetic Excitations And Fluctuations Ii written by Umberto Balucani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

An international workshop on Elementary Excitations and Fluctuations in Magnetic Systems was held in Turin for five days beginning 25 May, 1987. The workshop followed much the same format as the one with the same title held in San Miniato in 1984 (proceedings: Springer Series in-Solid-State Sciences, Vol. 54), that most participants contributed talks and provided papers for the proceedings. While many of the participants had attended the first workshop, 15 of the 40 invited review papers were presented by scientists who had not. The majority of the talks reported theoretical work concerned with the introduction of new techniques. However, experimental work was also well represented, not least because many of the reported theoretical studies were motivated by experimental findings, and a highlight of the workshop was an extremely stimulating session devoted to recent neutron scattering measure ments, on various systems, that exploited polarization analysis. The fine venue of the workshop, Villa Gualino, with its excellent facili ties and spacious accommodation, helped to produce a delightful relaxed and friendly atmosphere. For the use of Villa Gualino and significant financial support we are indebted to our host organization, the Institute for Scien tific Interchange (lSI). Additional financial support came from the Consiglio Nazionale delle Ricerche (CNR), Centro Interuniversitario di Struttura della Material del Ministero della Pubblica Istruzione (CISM-MPI) and Gruppo Nazionale di Struttura della Materia (GNSM-CNR).