Progress In High Dimensional Percolation And Random Graphs
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Progress In High Dimensional Percolation And Random Graphs
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Author : Markus Heydenreich
language : en
Publisher: Springer
Release Date : 2017-11-22
Progress In High Dimensional Percolation And Random Graphs written by Markus Heydenreich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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.
Fractal Geometry And Stochastics Vi
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Author : Uta Freiberg
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Fractal Geometry And Stochastics Vi written by Uta Freiberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
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.
In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius
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Author : Maria Eulália Vares
language : en
Publisher: Springer Nature
Release Date : 2021-03-25
In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius written by Maria Eulália Vares and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Mathematics categories.
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.
Sojourns In Probability Theory And Statistical Physics I
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Author : Vladas Sidoravicius
language : en
Publisher: Springer Nature
Release Date : 2019-10-17
Sojourns In Probability Theory And Statistical Physics I written by Vladas Sidoravicius and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-17 with Mathematics categories.
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.
The Nature Of Complex Networks
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Author : Sergey N. Dorogovtsev
language : en
Publisher: Oxford University Press
Release Date : 2022
The Nature Of Complex Networks written by Sergey N. Dorogovtsev and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Computers categories.
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 methods of 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.
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.
Coarse Geometry And Randomness
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Author : Itai Benjamini
language : en
Publisher: Springer
Release Date : 2013-12-02
Coarse Geometry And Randomness written by Itai Benjamini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-02 with Mathematics categories.
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).
Creative Complex Systems
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Author : Kazuo Nishimura
language : en
Publisher: Springer Nature
Release Date : 2021-10-26
Creative Complex Systems written by Kazuo Nishimura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-26 with Business & Economics categories.
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.
Probability And Statistical Physics In St Petersburg
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Author : V. Sidoravicius
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-28
Probability And Statistical Physics In St Petersburg written by V. Sidoravicius 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 2016-04-28 with Mathematics categories.
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.
Introduction To Random Graphs
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Author : Alan Frieze
language : en
Publisher: Cambridge University Press
Release Date : 2016
Introduction To Random Graphs written by Alan Frieze and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.