Download or read book Large Deviations for Random Graphs written by Sourav Chatterjee and published by Springer. This book was released on 2017-08-31 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.
Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2016-12-22 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
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.
Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2024-02-08 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive introduction to the local and global structure of random graph models for complex networks.
Download or read book Particle Systems Random Media and Large Deviations written by Richard Durrett and published by American Mathematical Soc.. This book was released on 1985 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the proceedings of the 1984 AMS Summer Research Conference. This work provides a summary of results from some of the areas in probability theory; interacting particle systems, percolation, random media (bulk properties and hydrodynamics), the Ising model and large deviations.
Download or read book Random Graphs written by Svante Janson and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references
Download or read book Stochastic Processes Modeling and Simulation written by D N Shanbhag and published by Gulf Professional Publishing. This book was released on 2003-02-24 with total page 1028 pages. Available in PDF, EPUB and Kindle. Book excerpt: This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.
Download or read book Random Graphs written by Béla Bollobás and published by Cambridge University Press. This book was released on 2001-08-30 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised and updated version of the classic first edition.
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 Large random matrices written by Alice Guionnet and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.
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.
Download or read book Handbook of Econometrics written by and published by Elsevier. This book was released on 2020-11-25 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Econometrics, Volume 7A, examines recent advances in foundational issues and "hot" topics within econometrics, such as inference for moment inequalities and estimation of high dimensional models. With its world-class editors and contributors, it succeeds in unifying leading studies of economic models, mathematical statistics and economic data. Our flourishing ability to address empirical problems in economics by using economic theory and statistical methods has driven the field of econometrics to unimaginable places. By designing methods of inference from data based on models of human choice behavior and social interactions, econometricians have created new subfields now sufficiently mature to require sophisticated literature summaries. Presents a broader and more comprehensive view of this expanding field than any other handbook Emphasizes the connection between econometrics and economics Highlights current topics for which no good summaries exist
Download or read book The Strange Logic of Random Graphs written by Joel Spencer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.
Download or read book On the Probability of Large Deviations of Random Variables written by I. N. Sanov and published by . This book was released on 1958 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Higher Order Systems written by Federico Battiston and published by Springer Nature. This book was released on 2022-04-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.
Download or read book Graph Theory and Additive Combinatorics written by Yufei Zhao and published by Cambridge University Press. This book was released on 2023-07-31 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
