We state some unsolved problems and describe relevant examples concerning randwom walks on trees. Most of the problems involve the behavior of random walks with drift: e.g., is the speed on Galton-Watson trees monotonic in the drift parameter? These random walks have been used in Monte-Carlo algorithms for sampling from 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 Galton-Watson trees satisfies an interesting functional equation; is this distribution function absolutely continuous?
CITATION STYLE
Lyons, R., Pemantle, R., & Peres, Y. (1997). Unsolved Problems Concerning Random Walks on Trees (pp. 223–237). https://doi.org/10.1007/978-1-4612-1862-3_18
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