Random Walk Covering of Some Special Trees
نویسنده
چکیده
For simple random walk on a finite tree, the cover time is the time taken to visit every vertex. For the balanced b-ary tree of height m, the cover time is shown to be asymptotic to 2mb(log b)/(b− 1) as m→∞. On the uniform random labeled tree on n vertices, we give a convincing heuristic argument that the mean time to cover and return to the root is asymptotic to 6(2π)n, and prove a weak O(n) upper bound. The argument rests upon a recursive formula for cover time of trees generated by a simple branching process. J. Math. Anal. Appl. 157 (1991) 271–283. ∗Research supported by N.S.F. Grant MCS87-01426
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