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Probability on Trees and Networks
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  • Title Probability on Trees and Networks
  • Author(s) Russell Lyons and Yuval Peres
  • Publisher: Cambridge University Press; 1 edition (January 20, 2017)
  • Hardcover 600 pages
  • eBook PDF
  • Language: English
  • ISBN-10/ASIN: 1107160154
  • ISBN-13: 978-1107160156
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Book Description

This book is concerned with certain aspects of discrete probability on infinite graphs that are currently in vigorous development. Of course, finite graphs are analyzed as well, but usually with the aim of understanding infinite graphs and networks. These areas of discrete probability are full of interesting, beautiful, and surprising results, many of which connect to other areas of mathematics and theoretical computer science. Numerous fascinating questions are still open.

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.

This authoritative state-of-the-art account of probability on networks for graduate students and researchers in mathematics, statistics, computer science, and engineering, brings together sixty years of research, including many developments where the authors played a leading role. The text emphasizes intuition, while also giving complete proofs.

About the Authors
  • Russell Lyons is James H. Rudy Professor of Mathematics at Indiana University, Bloomington. He obtained his PhD at the University of Michigan in 1983. He is a Fellow of the American Mathematical Society.
  • Yuval Peres is a Principal Researcher at Microsoft Research in Redmond, Washington. He obtained his PhD at the Hebrew University, Jerusalem in 1990. He is a fellow of the American Mathematical Society and a foreign associate member of the US National Academy of Sciences.
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