Classical and Modern Branching Processes
Volume 84 of the series The IMA Volumes in Mathematics and its Applications pp 223237
Unsolved Problems Concerning Random Walks on Trees
 Russell LyonsAffiliated withDepartment of Mathematics, Indiana University
 , Robin PemantleAffiliated withDepartment of Mathematics, University of Wisconsin
 , Yuval PeresAffiliated withDepartment of Statistics, University of California
Abstract
We state some unsolved problems and describe relevant examples concerning random walks on trees. Most of the problems involve the behavior of random walks with drift: e.g., is the speed on GaltonWatson trees monotonic in the drift parameter? These random walks have been used in MonteCarlo algorithms for sampling from the vertices of a tree; in general, their behavior reflects the size and regularity of the underlying tree. Random walks are related to conductance. The distribution function for the conductance of GaltonWatson trees satisfies an interesting functional equation; is this distribution function absolutely continuous?
Key words
GaltonWatson random walk speed rate of escape Title
 Unsolved Problems Concerning Random Walks on Trees
 Book Title
 Classical and Modern Branching Processes
 Pages
 pp 223237
 Copyright
 1997
 DOI
 10.1007/9781461218623_18
 Print ISBN
 9781461273158
 Online ISBN
 9781461218623
 Series Title
 The IMA Volumes in Mathematics and its Applications
 Series Volume
 84
 Series ISSN
 09406573
 Publisher
 Springer New York
 Copyright Holder
 Springer Science+Business Media New York
 Additional Links
 Topics
 Keywords

 GaltonWatson
 random walk
 speed
 rate of escape
 Industry Sectors
 eBook Packages
 Editors

 Krishna B. Athreya ^{(2)}
 Peter Jagers ^{(3)}
 Editor Affiliations

 2. Department of Mathematics and Statistics, Iowa State University
 3. School of Mathematics and Computing Science, Chalmers University of Technology, Gothenburg University
 Authors

 Russell Lyons ^{(4)}
 Robin Pemantle ^{(5)}
 Yuval Peres ^{(6)}
 Author Affiliations

 4. Department of Mathematics, Indiana University, Bloomington, IN, 474055701
 5. Department of Mathematics, University of Wisconsin, Madison, WI, 53706
 6. Department of Statistics, University of California, Berkeley, CA, 947203860
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