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arXiv · 0802.2248

Exact mean first-passage time on the T-graph

E. Agliari
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Abstract

We consider a simple random walk on the T-fractal and we calculate the exact mean time $τ^g$ to first reach the central node $i_0$. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except $i_0$. By means of analytic techniques based on decimation procedures, we find the explicit expression for $τ^g$ as a function of the generation $g$ and of the volume $V$ of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.

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E. Agliari. 2008-02-15. Exact mean first-passage time on the T-graph. https://doi.org/10.1103/physreve.77.011128

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