This book is still being written. All parts that are available are in close-to-finished form. Bibliographic references are not yet complete; feel free to help. We expect that the final product will be published by Cambridge University Press. However, we do not have a definite date for completion of the manuscript. When the book is done, that will be clearly noted here. Meanwhile, please do not ask Cambridge University Press how to obtain the book.

A few of the authors' results and proofs appear here for the first time. At this point, almost all of the actual writing was done by Lyons. We hope to have a more balanced co-authorship eventually.

Please let us know of any errors you find. In addition, suggestions for improvement of any sort, including exercises at any level, are welcome; please send them to rdlyons@indiana.edu or to peres [at] microsoft [dot] com.

You may wish to use the following if you refer to this book in a paper. Note in particular the correct method to get TeX to print a tilde.

\bibitem[Lyons with Peres (2012)]{LP:book}
\bibauthor{Lyons, R. {\rm with} Peres, Y.} (2012).
\newblock {\em Probability on Trees and Networks}.
\newblock Cambridge University Press.
\newblock In preparation. Current
  version available at \hfil\break
  {\tt http://mypage.iu.edu/\string~rdlyons/}.

Downloads and Extras:

• PDF file of the whole book (ix + 668 pages, 743 exercises, 9.3 megabytes).
• Higher-resolution versions of Figure 2.2, Figure 4.9, Figure 6.1, Figure 6.2, Figure 9.1, and Figure 10.2 as gzipped EPS files.
• A 3D UST (but the quality may be worse in your browser, depending on your plugin, than if you download and view it with a stand-alone player).
• A series of square tilings like the one below.

Chapter Titles:

Some Highlights
Random Walks and Electric Networks
Special Networks
Uniform Spanning Trees
Branching Processes, Second Moments, and Percolation
Isoperimetric Inequalities
Percolation on Transitive Graphs
The Mass-Transport Principle and Percolation
Infinite Electrical Networks and Dirichlet Functions
Uniform Spanning Forests
Minimal Spanning Forests
Limit Theorems for Galton-Watson Processes
Speed of Random Walks
Hausdorff Dimension
Capacity
Random Walks on Galton-Watson Trees
Tree-Indexed Processes (to be written)
Ising Models and Recursions (to be written)
Comments on Exercises
Bibliography
Index
Glossary of Notation

Information on updates:

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