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Author : Carina Betken
Publisher :
ISBN 13 :
Total Pages : 84 pages
Book Rating : 4.:/5 (115 download)
Download or read book Limit Theorems in Preferential Attachment Random Graphs written by Carina Betken and published by . This book was released on 2019 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1107118506
Total Pages : 483 pages
Book Rating : 4.1/5 (71 download)
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.
Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 110717287X
Total Pages : 341 pages
Book Rating : 4.1/5 (71 download)
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 2017 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.
Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.1/5 (394 download)
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.
Author : Svante Janson
Publisher : American Mathematical Soc.
ISBN 13 : 082182595X
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)
Download or read book Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics written by Svante Janson and published by American Mathematical Soc.. This book was released on 1994 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.
Author : Nathan B. Shank
Publisher :
ISBN 13 :
Total Pages : 202 pages
Book Rating : 4.:/5 (135 download)
Download or read book Limit Theorems for Random Euclidean Graphs written by Nathan B. Shank and published by . This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let cPon := {X1,..., XPon } be i.i.d. random points in Rd where Pon is an independent Poisson random variable with mean n. Recently Penrose [18] and Baryshnikov and Yukich [4] proved that under suitable conditions the finite dimensional distributions of re-normalized random point measures converge to a Gaussian field. These random point measures are defined in terms of a functional xi which acts on the random point set cPon . When the Xi have valued in [0,1] d I extend these results to show convergence of re-normalized centered random point measures as a process in D ([0,1] d). Additionally I consider the directed and undirected nearest neighbors graph on a collection of Pon points which are uniformly distributed on the Cantor set. I prove convergence to a constant of the re-scaled expected total edge length of this random graph. The re-scaling factor is a function of the fractal dimension and has a log periodic, non-constant behavior.
Author : Fan R. K. Chung
Publisher : American Mathematical Soc.
ISBN 13 : 0821836579
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)
Download or read book Complex Graphs and Networks written by Fan R. K. Chung and published by American Mathematical Soc.. This book was released on 2006 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.
Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 1316805581
Total Pages : 508 pages
Book Rating : 4.3/5 (168 download)
Download or read book Random Graphs and Complex Networks: Volume 2 written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2024-02-08 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.
Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 1107174007
Total Pages : 507 pages
Book Rating : 4.1/5 (71 download)
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.
Author : Fan R. K. Chung
Publisher : JHU Press
ISBN 13 : 9780821836576
Total Pages : 278 pages
Book Rating : 4.8/5 (365 download)
Download or read book Complex Graphs and Networks written by Fan R. K. Chung and published by JHU Press. This book was released on 2006 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.
Author : Sophia Saller
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (12 download)
Download or read book Local Limit Theorem in Random Graphs and Graphs on Non-constant Surfaces written by Sophia Saller and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Krishna B. Athreya
Publisher : Springer Science & Business Media
ISBN 13 : 3642653715
Total Pages : 301 pages
Book Rating : 4.6/5 (426 download)
Download or read book Branching Processes written by Krishna B. Athreya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.
Author : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1009260316
Total Pages : 234 pages
Book Rating : 4.0/5 (92 download)
Download or read book Random Graphs and Networks: A First Course written by Alan Frieze and published by Cambridge University Press. This book was released on 2023-03-09 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networks surround us, from social networks to protein–protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs – component structure, matchings and Hamilton cycles, connectivity and chromatic number – before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Author : Avrim Blum
Publisher : Cambridge University Press
ISBN 13 : 1108617360
Total Pages : 433 pages
Book Rating : 4.1/5 (86 download)
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.
Author : R. van der Hofstad
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (236 download)
Download or read book A Local Limit Theorem for the Critical Random Graph written by R. van der Hofstad and published by . This book was released on 2008 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hanan Baaqeel
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)
Download or read book Central Limit Theorems and Statistical Inference for Some Random Graph Models written by Hanan Baaqeel and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arup Bose
Publisher : CRC Press
ISBN 13 : 0429948891
Total Pages : 269 pages
Book Rating : 4.4/5 (299 download)
Download or read book Patterned Random Matrices written by Arup Bose and published by CRC Press. This book was released on 2018-05-23 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the March enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.
