V Sood et al 2005 J. Phys. A: Math. Gen. 38 109 doi:10.1088/0305-4470/38/1/007
V Sood1,3, S Redner1,3 and D ben-Avraham2
Show affiliationsWe study the mean time for a random walk to traverse between two arbitrary sites of the Erdős–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 behaviour can be understood by simple heuristic arguments.
05.40.Fb Random walks and Levy flights
02.10.Ox Combinatorics; graph theory
82B43 Percolation (See also 60K35)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 1 (7 January 2005)
Received 14 October 2004, in final form 28 October 2004
Published 8 December 2004
V Sood et al 2005 J. Phys. A: Math. Gen. 38 109
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