Exact mean first-passage time on the T-graph

Details Exact mean first-passage time on the T-graph Exact mean first-passage time on the T-graph

2008-02-15

arxiv.org/abs/0802.2248v1

Phys. Rev. E 77, 011128 (2008)

Physics

Data Analysis, Statistics and Probability

6 pages

Scientific paper

10.1103/PhysRevE.77.011128

We consider a simple random walk on the T-fractal and we calculate the exact mean time $\tau^g$ 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 $\tau^g$ 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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