Discrete Mathematics In Statistical Physics PDF Download
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| Author | : Martin Loebl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 187 |
| Release | : 2010-02-16 |
| Genre | : Science |
| ISBN | : 3834893293 |
Download Discrete Mathematics in Statistical Physics Book in PDF, ePub and Kindle
The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently. It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.
| Author | : Marc Mézard |
| Publisher | : Oxford University Press |
| Total Pages | : |
| Release | : 2009-01-22 |
| Genre | : Mathematics |
| ISBN | : 0191547190 |
Download Information, Physics, and Computation Book in PDF, ePub and Kindle
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances and adopts a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to study phase transitions.
| Author | : Jaroslav Nešetřil |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 218 |
| Release | : 2004 |
| Genre | : Science |
| ISBN | : 0821835513 |
Download Graphs, Morphisms and Statistical Physics Book in PDF, ePub and Kindle
Based on a March 2001 workshop, this collection explores connections between random graphs and percolation, between slow mixing and phase transition, and between graph morphisms and hard-constraint models. Topics of the 14 papers include efficient local search near phase transitions in combinatorial optimization, graph homomorphisms and long range action, recent results on parameterized H-colorings, the satisfiability of random k-Horn formulae, a discrete non-Pfaffian approach to the Ising problem, and chromatic numbers of products of tournaments. No indexes are provided. Annotation : 2004 Book News, Inc., Portland, OR (booknews.com).
| Author | : Harry Kesten |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 358 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662094444 |
Download Probability on Discrete Structures Book in PDF, ePub and Kindle
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
| Author | : Sacha Friedli |
| Publisher | : Cambridge University Press |
| Total Pages | : 643 |
| Release | : 2017-11-23 |
| Genre | : Mathematics |
| ISBN | : 1107184827 |
Download Statistical Mechanics of Lattice Systems Book in PDF, ePub and Kindle
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
| Author | : Jaroslav Neésetéril |
| Publisher | : |
| Total Pages | : 193 |
| Release | : 2004 |
| Genre | : Graph theory |
| ISBN | : 9781470440213 |
Download Graphs, Morphisms, and Statistical Physics Book in PDF, ePub and Kindle
The intersection of combinatorics and statistical physics has experienced great activity in recent years. This flurry of activity has been fertilized by an exchange not only of techniques, but also of objectives. Computer scientists interested in approximation algorithms have helped statistical physicists and discrete mathematicians overcome language problems. They have found a wealth of common ground in probabilistic combinatorics. Close connections between percolation and random graphs, graph morphisms and hard-constraint models, and slow mixing and phase transition have led to new results a.
| Author | : Allon Percus |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 394 |
| Release | : 2006 |
| Genre | : Computers |
| ISBN | : 9780195177374 |
Download Computational Complexity and Statistical Physics Book in PDF, ePub and Kindle
Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them. Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.
| Author | : Dénes Petz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 221 |
| Release | : 2007-10-20 |
| Genre | : Science |
| ISBN | : 3540746366 |
Download Quantum Information Theory and Quantum Statistics Book in PDF, ePub and Kindle
This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.
| Author | : Oliver Bühler |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 165 |
| Release | : 2006-10-12 |
| Genre | : Mathematical physics |
| ISBN | : 0821842323 |
Download A Brief Introduction to Classical, Statistical, and Quantum Mechanics Book in PDF, ePub and Kindle
This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006-07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods. The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is Hamilton-Jacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is self-contained. In particular, no previous knowledge of physics is assumed. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
| Author | : Bela Bollobas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 600 |
| Release | : 2010-05-17 |
| Genre | : Mathematics |
| ISBN | : 3540693955 |
Download Handbook of Large-Scale Random Networks Book in PDF, ePub and Kindle
With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the “Handbook of Graphs and Networks” published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.
