Percolation Theory For Mathematicians

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Percolation Theory for Mathematicians

Author : Kesten
Publisher : Springer Science & Business Media
ISBN 13 : 1489927301
Total Pages : 432 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Percolation Theory for Mathematicians by : Kesten

Download or read book Percolation Theory for Mathematicians written by Kesten and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quite apart from the fact that percolation theory had its orlgln in an honest applied problem (see Hammersley and Welsh (1980)), it is a source of fascinating problems of the best kind a mathematician can wish for: problems which are easy to state with a minimum of preparation, but whose solutions are (apparently) difficult and require new methods. At the same time many of the problems are of interest to or proposed by statistical physicists and not dreamt up merely to demons~te ingenuity. Progress in the field has been slow. Relatively few results have been established rigorously, despite the rapidly growing literature with variations and extensions of the basic model, conjectures, plausibility arguments and results of simulations. It is my aim to treat here some basic results with rigorous proofs. This is in the first place a research monograph, but there are few prerequisites; one term of any standard graduate course in probability should be more than enough. Much of the material is quite recent or new, and many of the proofs are still clumsy. Especially the attempt to give proofs valid for as many graphs as possible led to more complications than expected. I hope that the Applications and Examples provide justifi cation for going to this level of generality.

Percolation

Author : Geoffrey Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 1475742088
Total Pages : 304 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Percolation by : Geoffrey Grimmett

Download or read book Percolation written by Geoffrey Grimmett and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quite apart from the fact that percolation theory had its ongm in an honest applied problem, it is a source of fascinating problems of the best kind for which a mathematician can wish: problems which are easy to state with a minimum of preparation, but whose solutions are apparently difficult and require new methods. At the same time, many of the prob lems are of interest to or proposed by statistical physicists and not dreamed up merely to demonstrate ingenuity. Much progress has been made in recent years, and many of the open problems of ten years aga have been solved. With such solutions we have seen the evolution of new techniques and questions; the consequent knowledge has shifted the ground under percolation, and it is time to examine afresh the mathematics of the subject. The quantity of literature related to percolation seems to grow hour by hour, mostly in the physics journals. It is becoming increasingly diffi cult to get to know the subject from scratch, and one of the principal purposes of this book is to remedy this. This book is about the mathematics of percolation theory, with the emphasis upon presenting the shortest rigorous proofs of the main facts.

Percolation

Author : Geoffrey R. Grimmett
Publisher :
ISBN 13 : 9783662039823
Total Pages : 464 pages
Book Rating : 4.0/5 (398 download)

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Book Synopsis Percolation by : Geoffrey R. Grimmett

Download or read book Percolation written by Geoffrey R. Grimmett and published by . This book was released on 2014-01-15 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Percolation

Author : Geoffrey Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 9783540649021
Total Pages : 472 pages
Book Rating : 4.6/5 (49 download)

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Book Synopsis Percolation by : Geoffrey Grimmett

Download or read book Percolation written by Geoffrey Grimmett and published by Springer Science & Business Media. This book was released on 1999-05-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.

Applications of Percolation Theory

Author : Muhammad Sahimi
Publisher : Springer Nature
ISBN 13 : 3031203860
Total Pages : 690 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Applications of Percolation Theory by : Muhammad Sahimi

Download or read book Applications of Percolation Theory written by Muhammad Sahimi and published by Springer Nature. This book was released on 2023-03-18 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was published in 1994. Since then considerable progress has been made in both theoretical developments of percolation theory, and in its applications. The 2nd edition of this book is a response to such developments. Not only have all of the chapters of the 1st edition been completely rewritten, reorganized, and updated all the way to 2022, but also 8 new chapters have been added that describe extensive new applications, including biological materials, networks and graphs, directed percolation, earthquakes, geochemical processes, and large-scale real world problems, from spread of technology to ad-hoc mobile networks.

Percolation Theory and Ergodic Theory of Infinite Particle Systems

Author : Harry Kesten
Publisher : Springer Science & Business Media
ISBN 13 : 1461387345
Total Pages : 322 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Percolation Theory and Ergodic Theory of Infinite Particle Systems by : Harry Kesten

Download or read book Percolation Theory and Ergodic Theory of Infinite Particle Systems written by Harry Kesten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizing Committee, Harry Kesten (Chairman), Richard Holley, and Thomas Liggett for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinherger PREFACE Percolation theory and interacting particle systems both have seen an explosive growth in the last decade. These suhfields of probability theory are closely related to statistical mechanics and many of the publications on these suhjects (especially on the former) appear in physics journals, wit~ a great variahility in the level of rigour. There is a certain similarity and overlap hetween the methods used in these two areas and, not surprisingly, they tend to attract the same probabilists. It seemed a good idea to organize a workshop on "Percolation Theory and Ergodic Theory of Infinite Particle Systems" in the framework of the special probahility year at the Institute for Mathematics and its Applications in 1985-86. Such a workshop, dealing largely with rigorous results, was indeed held in February 1986.

Percolation

Author : Bela Bollobás
Publisher : Cambridge University Press
ISBN 13 : 0521872324
Total Pages : 334 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Percolation by : Bela Bollobás

Download or read book Percolation written by Bela Bollobás and published by Cambridge University Press. This book was released on 2006-09-21 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2006, is an account of percolation theory and its ramifications.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5396 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Introduction To Percolation Theory

Author : Dietrich Stauffer
Publisher : CRC Press
ISBN 13 : 1482272377
Total Pages : 192 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction To Percolation Theory by : Dietrich Stauffer

Download or read book Introduction To Percolation Theory written by Dietrich Stauffer and published by CRC Press. This book was released on 2018-12-10 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.

Applications of Percolation Theory, Second Edition

Author : Muhammad Sahimi
Publisher : CRC Press
ISBN 13 : 9781466513396
Total Pages : 500 pages
Book Rating : 4.5/5 (133 download)

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Book Synopsis Applications of Percolation Theory, Second Edition by : Muhammad Sahimi

Download or read book Applications of Percolation Theory, Second Edition written by Muhammad Sahimi and published by CRC Press. This book was released on 2014-09-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Percolation theory provides a mathematical framework for the study of random physical processes such as flow through disordered porous media. It spans applications in the physical sciences and beyond natural phenomena. Double in size, this second edition provides an up-to-date account of these applications. After reviewing the theory, the book covers a range of applications and variations. Well known in the field, the author presents examples in phase transitions, semiconductors, geology, astrophysics, network modeling, and the social sciences.

Probability on Graphs

Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Probability on Graphs by : Geoffrey Grimmett

Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Percolation Theory and Ergodic Theory of Infinite Particle Systems

Author : Harry Kesten
Publisher :
ISBN 13 : 9783540965374
Total Pages : 323 pages
Book Rating : 4.9/5 (653 download)

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Book Synopsis Percolation Theory and Ergodic Theory of Infinite Particle Systems by : Harry Kesten

Download or read book Percolation Theory and Ergodic Theory of Infinite Particle Systems written by Harry Kesten and published by . This book was released on 1987-01-01 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:

50 Years of First-Passage Percolation

Author : Antonio Auffinger
Publisher : American Mathematical Soc.
ISBN 13 : 1470441837
Total Pages : 169 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis 50 Years of First-Passage Percolation by : Antonio Auffinger

Download or read book 50 Years of First-Passage Percolation written by Antonio Auffinger and published by American Mathematical Soc.. This book was released on 2017-12-20 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: First-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. FPP was introduced in the 1960s as a random metric space. Although it is simple to define, and despite years of work by leading researchers, many of its central problems remain unsolved. In this book, the authors describe the main results of FPP, with two purposes in mind. First, they give self-contained proofs of seminal results obtained until the 1990s on limit shapes and geodesics. Second, they discuss recent perspectives and directions including (1) tools from metric geometry, (2) applications of concentration of measure, and (3) related growth and competition models. The authors also provide a collection of old and new open questions. This book is intended as a textbook for a graduate course or as a learning tool for researchers.

The Random-Cluster Model

Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 3540328912
Total Pages : 392 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Random-Cluster Model by : Geoffrey R. Grimmett

Download or read book The Random-Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.

Percolation Theory for Flow in Porous Media

Author : Allen Hunt
Publisher : Springer Science & Business Media
ISBN 13 : 3540897895
Total Pages : 334 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Percolation Theory for Flow in Porous Media by : Allen Hunt

Download or read book Percolation Theory for Flow in Porous Media written by Allen Hunt and published by Springer Science & Business Media. This book was released on 2009-05-05 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why would we wish to start a 2nd edition of “Percolation theory for ?ow in porous media” only two years after the ?rst one was ?nished? There are essentially three reasons: 1) Reviews in the soil physics community have pointed out that the introductory material on percolation theory could have been more accessible. Our additional experience in teaching this material led us to believe that we could improve this aspect of the book. In the context of rewriting the ?rst chapter, however, we also expanded the discussion of Bethe lattices and their relevance for “classical” - ponents of percolation theory, thus giving more of a basis for the discussion of the relevance of hyperscaling. This addition, though it will not tend to make the book more accessible to hydrologists, was useful in making it a more complete reference, and these sections have been marked as being possible to omit in a ?rst reading. It also forced a division of the ?rst chapter into two. We hope that physicists without a background in percolation theory will now also ?nd the - troductory material somewhat more satisfactory. 2) We have done considerable further work on problems of electrical conductivity, thermal conductivity, and electromechanical coupling.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Probability Theory

Author : Achim Klenke
Publisher : Springer Science & Business Media
ISBN 13 : 1848000480
Total Pages : 621 pages
Book Rating : 4.8/5 (48 download)

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Book Synopsis Probability Theory by : Achim Klenke

Download or read book Probability Theory written by Achim Klenke and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.