Gibbs Measures And Phase Transitions On Locally Tree Like Graphs
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| Author | : Hans-Otto Georgii |
| Publisher | : Walter de Gruyter |
| Total Pages | : 561 |
| Release | : 2011 |
| Genre | : Measure theory |
| ISBN | : 3110250292 |
From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert." (F. Papangelou
| Author | : Vladas Sidoravicius |
| Publisher | : Springer Nature |
| Total Pages | : 348 |
| Release | : 2019-10-17 |
| Genre | : Mathematics |
| ISBN | : 9811502943 |
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
| Author | : Geoffrey Grimmett |
| Publisher | : Cambridge University Press |
| Total Pages | : 279 |
| Release | : 2018-01-25 |
| Genre | : Mathematics |
| ISBN | : 1108542999 |
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
| Author | : Remco van der Hofstad |
| Publisher | : Cambridge University Press |
| Total Pages | : 507 |
| Release | : 2024-02-08 |
| Genre | : Mathematics |
| ISBN | : 1107174007 |
The definitive introduction to the local and global structure of random graph models for complex networks.
| Author | : Ross Kindermann |
| Publisher | : |
| Total Pages | : 160 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : |
The study of Markov random fields has brought exciting new problems to probability theory which are being developed in parallel with basic investigation in other disciplines, most notably physics. The mathematical and physical literature is often quite technical. This book aims at a more gentle introduction to these new areas of research.
| Author | : Imre Bárány |
| Publisher | : Springer Nature |
| Total Pages | : 616 |
| Release | : 2020-02-04 |
| Genre | : Mathematics |
| ISBN | : 3662592045 |
This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of László Lovász. The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization. László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, “building bridges” between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to László Lovász's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.
| Author | : Hans-Otto Georgii |
| Publisher | : Walter de Gruyter |
| Total Pages | : 561 |
| Release | : 2011-05-31 |
| Genre | : Mathematics |
| ISBN | : 3110250322 |
"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
| Author | : Marc Mézard |
| Publisher | : Oxford University Press |
| Total Pages | : 584 |
| Release | : 2009-01-22 |
| Genre | : Computers |
| ISBN | : 019857083X |
A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.
| Author | : Utkir A Rozikov |
| Publisher | : World Scientific |
| Total Pages | : 367 |
| Release | : 2022-07-28 |
| Genre | : Mathematics |
| ISBN | : 9811251258 |
This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
| Author | : Dmitry Panchenko |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 164 |
| Release | : 2013-02-26 |
| Genre | : Mathematics |
| ISBN | : 1461462894 |
The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.
