Asymptotic analysis of first passage time in complex networks - Condensed Matter > Statistical Mechanics

Abstract: The first passage time FPT distribution for random walk in complex networksis calculated through an asymptotic analysis. For network with size $N$ andshort relaxation time $\tau\ll N$, the computed mean first passage time MFPT,which is inverse of the decay rate of FPT distribution, is inverselyproportional to the degree of the destination. These results are verifiednumerically for the paradigmatic networks with excellent agreement. We showthat the range of validity of the analytical results covers networks that haveshort relaxation time and high mean degree, which turn out to be valid to manyreal networks.

Author: Hon Wai Lau, Kwok Yip Szeto

Source: https://arxiv.org/