Cambridge University Press eBooks· 2016
Probability on Trees and Networks
- 860citations
- 2016year
Short summary
This book synthesizes decades of research connecting graph geometry with stochastic processes, presenting a unified account of probability on networks.
AI-generated from the title and abstract; the full text is not read.
Key points
- Connects graph geometry with stochastic processes on graphs.
- Covers percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks.
- Includes recent developments like uniform spanning forests and mass-transport technique.
- Features over 850 exercises and emphasizes intuition with complete proofs.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2016 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics