
Random Walks and Heat Kernels on Graphs
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Reviews / Votes
'This book, written with great care, is a comprehensive course on random walks on graphs, with a focus on the relation between rough geometric properties of the underlying graph and the asymptotic behavior of the random walk on it. It is accessible to graduate students but may also serve as a good reference for researchers. It contains the usual material about random walks on graphs and its connections to discrete potential theory and electrical resistance (Chapters 1, 2 and 3). The heart of the book is then devoted to the study of the heat kernel (Chapters 4, 5 and 6). The author develops sufficient conditions under which sub-Gaussian or Gaussian bounds for the heat kernel hold (both on-diagonal and off diagonal; both upper and lower bounds).' Nicolas Curien, Mathematical Review 'The book under review delineates very thoroughly the general theory of random walks on weighted graphs. The author's expertise in both probability and analysis is apparent in the exposition and the elegant proofs depicted in the book.' Eviatar B. Procaccia, Bulletin of the American Mathematical SocietyMore details
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