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Progress In High Dimensional Percolation And Random Graphs
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Book Synopsis Progress in High-Dimensional Percolation and Random Graphs by : Markus Heydenreich
Download or read book Progress in High-Dimensional Percolation and Random Graphs written by Markus Heydenreich and published by Springer. This book was released on 2017-11-22 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime nsional percolation. Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.
Book Synopsis Fractal Geometry and Stochastics VI by : Uta Freiberg
Download or read book Fractal Geometry and Stochastics VI written by Uta Freiberg and published by Springer Nature. This book was released on 2021-03-23 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.
Book Synopsis In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius by : Maria Eulália Vares
Download or read book In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius written by Maria Eulália Vares and published by Springer Nature. This book was released on 2021-03-25 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.
Book Synopsis Sojourns in Probability Theory and Statistical Physics - I by : Vladas Sidoravicius
Download or read book Sojourns in Probability Theory and Statistical Physics - I written by Vladas Sidoravicius and published by Springer Nature. This book was released on 2019-10-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Nature of Complex Networks by : Sergey N. Dorogovtsev
Download or read book The Nature of Complex Networks written by Sergey N. Dorogovtsev and published by Oxford University Press. This book was released on 2022 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Nature of Complex Networks provides a systematic introduction to the statistical mechanics of complex networks and the different theoretical achievements in the field that are now finding strands in common.The book presents a wide range of networks and the processes taking place on them, including recently developed directions, methods, and techniques. It assumes a statistical mechanics view of random networks based on the concept of statistical ensembles but also features the approaches and methodsof modern random graph theory and their overlaps with statistical physics.This book will appeal to graduate students and researchers in the fields of statistical physics, complex systems, graph theory, applied mathematics, and theoretical epidemiology.
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
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.
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.
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.
Book Synopsis Introduction to Random Graphs by : Alan Frieze
Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Book Synopsis Coarse Geometry and Randomness by : Itai Benjamini
Download or read book Coarse Geometry and Randomness written by Itai Benjamini and published by Springer. This book was released on 2013-12-02 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ).
Book Synopsis Creative Complex Systems by : Kazuo Nishimura
Download or read book Creative Complex Systems written by Kazuo Nishimura and published by Springer Nature. This book was released on 2021-10-26 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, problems such as environmental and economic crises and pandemics caused by new viruses have been occurring on a global scale. Globalization brings about benefits, but it can increase the potential risks of “systemic problems”, leading to system-wide disruptions. The coronavirus pandemic, declared on March 11, 2020, by the World Health Organization, has revealed social disparities in the form of a higher risk of death for people of low-socioeconomic status and has caused massive destruction of the economy and of globalization itself. Extensive efforts to cope with these challenges have often led to the emergence of additional problems due to the chain of hidden causation. What can be done to protect against such emerging challenges? Despite the resulting complexity, once these individual problems are considered as different aspects of a single whole, seemingly contradictory issues can become totally understandable, as they can be integrated into a single coherent framework. This is the integrationist approach in contrast to the reductionist approach. Situations of this kind are truly relevant to understanding the question, “What are creative complex systems?” This book features contributions by members and colleagues of the Kyoto University International Research Unit of Integrated Complex System Science. It broadens our outlook from the traditional view of stability, in which global situations are eventually stabilized after the impact of destruction, to “creative” complex systems.
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.
Book Synopsis Probability and Statistical Physics in St. Petersburg by : V. Sidoravicius
Download or read book Probability and Statistical Physics in St. Petersburg written by V. Sidoravicius and published by American Mathematical Soc.. This book was released on 2016-04-28 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Book Synopsis Percolation by : Geoffrey R. Grimmett
Download or read book Percolation written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 459 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.
Book Synopsis Foundations of Data Science by : Avrim Blum
Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.
Book Synopsis Information, Physics, and Computation by : Marc Mézard
Download or read book Information, Physics, and Computation written by Marc Mézard and published by Oxford University Press. This book was released on 2009-01-22 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
