Mean first-passage time for random walks on the T-graph

Details Mean first-passage time for random walks on the T-graph Mean first-passage time for random walks on the T-graph

2009-07-19

arxiv.org/abs/0907.3251v2

New Journal of Physics, 2009, 11: 103043

Physics

Condensed Matter

Statistical Mechanics

Definitive version accepted for publication in New Journal of Physics

Scientific paper

10.1088/1367-2630/11/10/103043

For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks in the famous T-graph, linking this important quantity to the resistance distance in electronic networks. We obtain an exact formula for the MFPT that is confirmed by extensive numerical calculations. The interesting quantity is derived through the recurrence relations resulting from the self-similar structure of the T-graph. The obtained closed-form expression exhibits that the MFPT approximately increases as a power-law function of the number of nodes, with the exponent lying between 1 and 2. Our research may shed light on the deeper understanding of random walks on the T-graph.

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