Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-10-12
J. Phys. A 38, 109-123 (2005)
Physics
Condensed Matter
Statistical Mechanics
10 pages, 9 figures, 2-column revtex4 format
Scientific paper
10.1088/0305-4470/38/1/007
We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.
ben-Avraham Daniel
Redner Sid
Sood Vishal
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