Asymptotic Expansion Of A Partition Function Related To The Sinh Model

Author : Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski
Publisher : Springer
Page : 222 pages
File Size : 40,9 Mb
Release : 2016-12-08
Category : Science
ISBN : 9783319333793

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Asymptotic Expansion of a Partition Function Related to the Sinh-model by Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski Pdf

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.

Author : Alice Guionnet
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 55,6 Mb
Release : 2019-04-29
Category : Green's functions
ISBN : 9781470450274

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Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations by Alice Guionnet Pdf

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.

Author : Pavel Bleher, Karl Liechty
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 52,8 Mb
Release : 2013-12-04
Category : Mathematics
ISBN : 9781470409616

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Random Matrices and the Six-Vertex Model by Pavel Bleher, Karl Liechty Pdf

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.

Author : Anonim
Publisher : ScholarlyEditions
Page : 864 pages
File Size : 45,9 Mb
Release : 2012-01-09
Category : Mathematics
ISBN : 9781464965067

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Issues in Applied Mathematics: 2011 Edition by Anonim Pdf

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/.

Author : INSTITUTE OF PHYSICS. (Great Britain). AMERICAN INSTITUTE OF PHYSICS. (USA)
Publisher : Unknown
Page : 292 pages
File Size : 42,5 Mb
Release : 2002
Category : Mathematical physics
ISBN : 03054470

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Journal of Physics A. Mathematical and General by INSTITUTE OF PHYSICS. (Great Britain). AMERICAN INSTITUTE OF PHYSICS. (USA) Pdf

Author : Stephane Ouvry,Vincent Pasquier,Didina Serban,Leticia Cugliandolo
Publisher : Oxford University Press
Page : 651 pages
File Size : 47,9 Mb
Release : 2010-04-22
Category : Language Arts & Disciplines
ISBN : 9780199574612

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Exact Methods in Low-dimensional Statistical Physics and Quantum Computing by Stephane Ouvry,Vincent Pasquier,Didina Serban,Leticia Cugliandolo Pdf

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 of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.

Author : Geoffrey B. Campbell
Publisher : CRC Press
Page : 567 pages
File Size : 55,6 Mb
Release : 2024-05-29
Category : Mathematics
ISBN : 9781040026441

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Vector Partitions, Visible Points and Ramanujan Functions by Geoffrey B. Campbell Pdf

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.

Author : Claudio Pellegrini,Paola Cerrai,Paolo Freguglia
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461505914

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The Application of Mathematics to the Sciences of Nature by Claudio Pellegrini,Paola Cerrai,Paolo Freguglia Pdf

The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication. The goal of the meeting and the papers collected in this proceedings volume is to give physicists, biologists, mathematicians, and historians of science the opportunity to share information on their work and reflect on the and mathematical models are used in the natural sciences today and in way mathematics the past. The program of the workshop combines the experience of those working on current scientific research in many different fields with the historical analysis of previous results. We hope that some novel interdisciplinary, philosophical, and epistemological considerations will follow from the two aspects of the workshop, the historical and the scientific· This proceedings includes papers presented at the meeting and some of the results of the discussions that took place during the workshop. We wish to express our gratitude to Sergio Monteiro for all his work, which has been essential for the successful publication of these proceedings. We also want to thank the editors of Kluwer AcademidPlenum Publishers for their patience and constant help, and in particular Beth Kuhne and Roberta Klarreich. Our thanks to the fallowing institutions: -Amministrazione Comunale di Arcidosso -Comunita Montana del Monte Amiata ·Center for the History of Physics, UCLA -Centre F.

Author : Ilya Prigogine,Stuart A. Rice
Publisher : John Wiley & Sons
Page : 458 pages
File Size : 49,7 Mb
Release : 2009-09-09
Category : Science
ISBN : 9780470142240

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Advances in Chemical Physics, Volume 112 by Ilya Prigogine,Stuart A. Rice Pdf

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)

Author : George E. Andrews,Bruce C. Berndt
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 46,6 Mb
Release : 2012-06-08
Category : Mathematics
ISBN : 9781461438106

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Ramanujan's Lost Notebook by George E. Andrews,Bruce C. Berndt Pdf

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the third of five volumes that the authors plan to write on Ramanujan’s lost notebook and other manuscripts and fragments found in The Lost Notebook and Other Unpublished Papers, published by Narosa in 1988. The ordinary partition function p(n) is the focus of this third volume. In particular, ranks, cranks, and congruences for p(n) are in the spotlight. Other topics include the Ramanujan tau-function, the Rogers–Ramanujan functions, highly composite numbers, and sums of powers of theta functions. Review from the second volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited." - MathSciNet Review from the first volume: "Andrews a nd Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society

Author : Michio Kaku,Antal Jevicki,Keiji Kikkawa
Publisher : World Scientific
Page : 436 pages
File Size : 51,5 Mb
Release : 1991-04-30
Category : Electronic
ISBN : 9789814569286

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Quarks, Symmetries And Strings - A Symposium In Honor Of Bunji Sakita's 60th Birthday by Michio Kaku,Antal Jevicki,Keiji Kikkawa Pdf

Quarks, Symmetries and Strings is a book that reflects the rich diversity of current research in physics: it describes quantum chromodynamics, quark phenomenology, superstring theory, supersymmetry, matrix models, statistical methods, superconductivity and neural networks. The book also reflects the diversity of Dr Bunji Sakita's scientific work. Dr Sakita has made seminal contributions in many of these areas. The book celebrates the many path-breaking ideas he pioneered which still cross-fertilize many of the most active areas of current research.

Author : Umberto Balucani,Stephen W. Lovesey,Mario G. Rasetti,Valerio Tognetti
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642731075

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Magnetic Excitations and Fluctuations II by Umberto Balucani,Stephen W. Lovesey,Mario G. Rasetti,Valerio Tognetti Pdf

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).

Author : Frank W. J. Olver
Publisher : Cambridge University Press
Page : 968 pages
File Size : 53,6 Mb
Release : 2010-05-17
Category : Mathematics
ISBN : 9780521192255

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NIST Handbook of Mathematical Functions Hardback and CD-ROM by Frank W. J. Olver Pdf

The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

Author : L.J. de Jongh
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400918603

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Magnetic Properties of Layered Transition Metal Compounds by L.J. de Jongh Pdf

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.

Author : Holly Marie Swisher
Publisher : Unknown
Page : 64 pages
File Size : 46,9 Mb
Release : 2005
Category : Electronic
ISBN : WISC:89092042001

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Asymptotics and Congruence Properties for Stanley's Partition Function, and a Note on a Theorem of Koike by Holly Marie Swisher Pdf