On the first passage time of a simple random walk on a tree

We consider a simple random walk on a tree. Exact expressions are obtained for the expectation and the variance of the first passage time, thereby recovering the known result that these are integers. A relationship of the mean first passage matrix with the distance matrix is established and used to...

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Bibliographic Details
Published in:Statistics & probability letters 2011-10, Vol.81 (10), p.1552-1558
Main Author: Bapat, R.B.
Format: Article
Language:English
Subjects:
Distance matrix
Exact sciences and technology
General topics
Laplacian matrix
Linear inference, regression
Mathematics
Mean first passage matrix
Probability and statistics
Probability theory and stochastic processes
Random walk
Random walk Tree Mean first passage matrix Distance matrix Laplacian matrix
Sciences and techniques of general use
Statistics
Stochastic processes
Tree
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Summary:We consider a simple random walk on a tree. Exact expressions are obtained for the expectation and the variance of the first passage time, thereby recovering the known result that these are integers. A relationship of the mean first passage matrix with the distance matrix is established and used to derive a formula for the inverse of the mean first passage matrix.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2011.05.017