[PDF] Probability On Trees And Networks eBook

Author : Russell Lyons
Publisher : Cambridge University Press
Page : 1023 pages
File Size : 28,11 MB
Release : 2017-01-20
Category : Mathematics
ISBN : 1316785335

GET BOOK

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Author : Geoffrey Grimmett
Publisher : Cambridge University Press
Page : 279 pages
File Size : 36,64 MB
Release : 2018-01-25
Category : Mathematics
ISBN : 1108542999

GET BOOK

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.

Author : Steven N. Evans
Publisher : Springer
Page : 205 pages
File Size : 46,54 MB
Release : 2007-09-26
Category : Mathematics
ISBN : 3540747982

GET BOOK

Random trees and tree-valued stochastic processes are of particular importance in many fields. Using the framework of abstract "tree-like" metric spaces and ideas from metric geometry, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behavior of such objects when the number of vertices goes to infinity. This publication surveys the relevant mathematical background and present some selected applications of the theory.

Author : S. R. Kingan
Publisher : John Wiley & Sons
Page : 292 pages
File Size : 37,34 MB
Release : 2022-04-28
Category : Mathematics
ISBN : 1118937279

GET BOOK

Graphs and Networks A unique blend of graph theory and network science for mathematicians and data science professionals alike. Featuring topics such as minors, connectomes, trees, distance, spectral graph theory, similarity, centrality, small-world networks, scale-free networks, graph algorithms, Eulerian circuits, Hamiltonian cycles, coloring, higher connectivity, planar graphs, flows, matchings, and coverings, Graphs and Networks contains modern applications for graph theorists and a host of useful theorems for network scientists. The book begins with applications to biology and the social and political sciences and gradually takes a more theoretical direction toward graph structure theory and combinatorial optimization. A background in linear algebra, probability, and statistics provides the proper frame of reference. Graphs and Networks also features: Applications to neuroscience, climate science, and the social and political sciences A research outlook integrated directly into the narrative with ideas for students interested in pursuing research projects at all levels A large selection of primary and secondary sources for further reading Historical notes that hint at the passion and excitement behind the discoveries Practice problems that reinforce the concepts and encourage further investigation and independent work

Author : Asaf Nachmias
Publisher : Springer Nature
Page : 120 pages
File Size : 34,23 MB
Release : 2019-10-04
Category : Mathematics
ISBN : 3030279685

GET BOOK

This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

Author : Peter G. Doyle
Publisher : American Mathematical Soc.
Page : 159 pages
File Size : 24,14 MB
Release : 1984-12-31
Category : Electric network topology
ISBN : 1614440220

GET BOOK

Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 341 pages
File Size : 50,36 MB
Release : 2017
Category : Computers
ISBN : 110717287X

GET BOOK

This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Author : Michael Drmota
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 23,60 MB
Release : 2009-04-16
Category : Mathematics
ISBN : 3211753575

GET BOOK

The aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.

Author : Christopher J. Bishop
Publisher : Cambridge University Press
Page : 415 pages
File Size : 15,5 MB
Release : 2017
Category : Mathematics
ISBN : 1107134110

GET BOOK

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Author : Wolfgang Woess
Publisher : Cambridge University Press
Page : 350 pages
File Size : 29,4 MB
Release : 2000-02-13
Category : Mathematics
ISBN : 0521552923

GET BOOK

The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.