Probability on trees and networks /
Lyons, Russell,
Probability on trees and networks / Russell Lyons, Indiana University, Bloomington, Yuval Peres, Microsoft Research, Redmond, Washington. - New York : Cambridge University Press, 2016. - 1 online resource (xv, 698 pages) : digital, PDF file(s). - Cambridge series in statistical and probabilistic mathematics ; 42 . - Cambridge series on statistical and probabilistic mathematics ; 42. .
Title from publisher's bibliographic system (viewed on 31 Jan 2017).
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.
9781316672815 (ebook)
Stochastic processes.
Trees (Graph theory)
QA274 / .L956 2016
511/.52
Probability on trees and networks / Russell Lyons, Indiana University, Bloomington, Yuval Peres, Microsoft Research, Redmond, Washington. - New York : Cambridge University Press, 2016. - 1 online resource (xv, 698 pages) : digital, PDF file(s). - Cambridge series in statistical and probabilistic mathematics ; 42 . - Cambridge series on statistical and probabilistic mathematics ; 42. .
Title from publisher's bibliographic system (viewed on 31 Jan 2017).
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.
9781316672815 (ebook)
Stochastic processes.
Trees (Graph theory)
QA274 / .L956 2016
511/.52