Random Walks on Infinite Graphs and Groups (Cambridge Tracts in Mathematics, Series Number 138) 1st Edition by Wolfgang Woess (PDF)

Description

This eminent work focuses on the interplay between the behavior of random walks and discrete structure theory. Wolfgang Woess considers Markov chains whose state space is equipped with the structure of an infinite, locally-finite graph, or of a finitely generated group. He assumes the transition probabilities are adapted to the underlying structure in some way that must be specified precisely in each case. He also explores the impact the particular type of structure has on various aspects of the behavior of the random walk. In addition, the author shows how random walks are useful tools for classifying, or at least describing, the structure of graphs and groups.

User’s Reviews

Editorial Reviews: Review “The organization of the book is well-thought-out…The reviewer has a very high opition of this book” Bulletin of the American Mathematical Society”a very valuable addition to the literture on this fascinating and important subject.” Mathematical Review Book Description The main theme of this book is the interplay between random walks and discrete structure theory.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I feel compelled to give this 5 stars, simply for the fact that this book compiles a mammoth amount of information which is otherwise only available scattered around dozens of papers. This was clearly a major effort, and it’s a great reference on the uses of Markov chains in geometric group theory and discrete geometry. This is a book I’ll definitely come back to.That said, this book is not for the faint of heart. The index is laughably awful, and the author is very careful not to repeat any definitions, so I found myself needing an excessive amount of bookmarks and marginalia to follow the text. The writing is denser than a neutron star in a mechanical vise, even by the standards of graduate level math books. The text is downright impenetrable at times; to convince yourself of all the offhand statements that Woess makes in a given page can easily take hours.If you need it for your research, it’s an invaluable alternative to digging through piles of papers. But be warned, it’s a hard book.

⭐This book is difficult for self-study – and the author says so in his preface! I felt, the prerequities in probablity theory and in graph theory are relatively modest (Prof. Bollobas’ book is much more than adequate!), but a excellent knowledge in group theory will very definitely help. For the last chapter, some knowledge in topology would be advantageous, too.There is no doubt, that Prof. Woess is an expert in this field, and the various methods employed to proof theorems are very interesting, and often “unexpected”.If there is a point to critizise, it is the relative lack of examples, showing where the stuff proved might be employed, also a few figures to help visualize certain concepts might have added to the book.The book contains an “average” number of typos, I counted about 40 or so, mostly of a harmless nature.For anybody interested in random walks, with a GOOD knowledge of group theory I can thouroughly recommend this book.

⭐

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