On the first passage time of a simple random walk on a tree |
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Authors: | RB Bapat |
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Institution: | Indian Statistical Institute, New Delhi, 110016, India |
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Abstract: | 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. |
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Keywords: | Random walk Tree Mean first passage matrix Distance matrix Laplacian matrix |
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