Percolation Theory For Mathematicians
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Percolation Theory For Mathematicians
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Author : Harry Kesten
language : en
Publisher:
Release Date : 1982
Percolation Theory For Mathematicians written by Harry Kesten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Science categories.
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 demons̃te 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 Theory For Mathematicians
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Author : Kesten
language : en
Publisher:
Release Date : 2014-01-15
Percolation Theory For Mathematicians written by Kesten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Percolation Theory For Mathematicians
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Author : Kesten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Percolation Theory For Mathematicians written by Kesten 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 2013-11-11 with Mathematics categories.
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
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Author : Geoffrey R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Percolation written by Geoffrey R. Grimmett 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 2013-03-09 with Mathematics categories.
Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed. 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.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
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.
Percolation
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Author : Geoffrey R. Grimmett
language : en
Publisher:
Release Date : 2014-01-15
Percolation written by Geoffrey R. Grimmett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
50 Years Of First Passage Percolation
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Author : Antonio Auffinger
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-20
50 Years Of First Passage Percolation written by Antonio Auffinger 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 2017-12-20 with Mathematics categories.
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.
Percolation
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Author : Geoffrey Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Percolation written by Geoffrey Grimmett 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 2013-03-09 with Science categories.
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.
Introduction To Percolation Theory
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Author : A. Aharony
language : en
Publisher: Taylor & Francis
Release Date : 2003-07-13
Introduction To Percolation Theory written by A. Aharony and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-13 with Science categories.
Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions and disordered systems. It provides a quantitative model for understanding these phenomena, and therefore a theoretical and statistical background to many physical and natural sciences. This book explains the basic theory for the graduate while also reaching into the specialized fields of disordered systems and renormalization groups. Much of the book deals with systems lying close to the critical point phase transition point, where the subject is at its most interesting and sensitive. This text is ideal for those who deal with systems which exhibit critical points and phase transition behavior.
Percolation Theory Using Python
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Author : Anders Malthe-Sørenssen
language : en
Publisher: Springer Nature
Release Date : 2024-06-29
Percolation Theory Using Python written by Anders Malthe-Sørenssen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-29 with Science categories.
This course-based open access textbook delves into percolation theory, examining the physical properties of random media—materials characterized by varying sizes of holes and pores. The focus is on both the mathematical foundations and the computational and statistical methods used in this field. Designed as a practical introduction, the book places particular emphasis on providing a comprehensive set of computational tools necessary for studying percolation theory. Readers will learn how to generate, analyze, and comprehend data and models, with detailed theoretical discussions complemented by accessible computer codes. The book's structure ensures a complete exploration of worked examples, encompassing theory, modeling, implementation, analysis, and the resulting connections between theory and analysis. Beginning with a simplified model system—a model porous medium—whose mathematical theory is well-established, the book subsequently applies the same framework to realistic random systems. Key topics covered include one- and infinite-dimensional percolation, clusters, scaling theory, diffusion in disordered media, and dynamic processes. Aimed at graduate students and researchers, this textbook serves as a foundational resource for understanding essential concepts in modern statistical physics, such as disorder, scaling, and fractal geometry.