Random Walks And Electric Networks
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Random Walks And Electric Networks
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Author : Peter G. Doyle
language : en
Publisher: American Mathematical Soc.
Release Date : 1984-12-31
Random Walks And Electric Networks written by Peter G. Doyle 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 1984-12-31 with Electric network topology categories.
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.
Random Walks And Electric Networks
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Author : Peter G. Doyle
language : en
Publisher:
Release Date : 1984
Random Walks And Electric Networks written by Peter G. Doyle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Electric network topology categories.
Random Walks And Diffusions On Graphs And Databases
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Author : Philippe Blanchard
language : en
Publisher: Springer
Release Date : 2013-07-15
Random Walks And Diffusions On Graphs And Databases written by Philippe Blanchard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-15 with Science categories.
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Random Walks On Infinite Graphs And Groups
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Author : Wolfgang Woess
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Random Walks On Infinite Graphs And Groups written by Wolfgang Woess 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 2000-02-13 with Mathematics categories.
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.
Inverse Problems For Electrical Networks
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Author : Edward B Curtis
language : en
Publisher: World Scientific
Release Date : 2000-03-02
Inverse Problems For Electrical Networks written by Edward B Curtis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-02 with Mathematics categories.
This book is a very timely exposition of part of an important subject which goes under the general name of “inverse problems”. The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors' analysis of this similar problem for resistor networks.The authors' treatment of inverse problems for electrical networks is at a fairly elementary level. It is accessible to advanced undergraduates, and mathematics students at the graduate level. The topics are of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment. It is this amalgamation of such topics as graph theory, medial graphs and matrix algebra, as well as the analogy to inverse problems for partial differential equations, that makes the book both original and interesting.
Random Walks And Heat Kernels On Graphs
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Author : M. T. Barlow
language : en
Publisher: Cambridge University Press
Release Date : 2017-02-23
Random Walks And Heat Kernels On Graphs written by M. T. Barlow 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 2017-02-23 with Mathematics categories.
Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Two Dimensional Random Walk
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Author : Serguei Popov
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-18
Two Dimensional Random Walk written by Serguei Popov 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 2021-03-18 with Mathematics categories.
The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. It starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. After reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements - which can be viewed as a 'canonical soup' of nearest-neighbour loops through infinity - again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks - which are the 'noodles' in the soup - and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making it suitable for courses and independent study.
Random Walks And Electric Networks
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Author : Mohamad Kassab
language : en
Publisher:
Release Date : 2010
Random Walks And Electric Networks written by Mohamad Kassab and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Harmonic analysis categories.
Modern Graph Theory
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Author : Béla Bollobás
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-07
Modern Graph Theory written by Béla Bollobás 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 1998-07 with Computers categories.
An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
Stochastic Networks
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Author : Frank Kelly
language : en
Publisher: Cambridge University Press
Release Date : 2014-02-27
Stochastic Networks written by Frank Kelly 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 2014-02-27 with Computers categories.
A compact, highly-motivated introduction to some of the stochastic models found useful in the study of communications networks.