Heterogeneous Mean First-Passage Time Scaling in Fractal Media

Hyun Myung Chun, Sungmin Hwang, Byungnam Kahng, Heiko Rieger, Jae Dong Noh

Research output: Contribution to journalArticlepeer-review


The mean first passage time (MFPT) of random walks is a key quantity characterizing dynamic processes on disordered media. In a random fractal embedded in the Euclidean space, the MFPT is known to obey the power law scaling with the distance between a source and a target site with a universal exponent. We find that the scaling law for the MFPT is not determined solely by the distance between a source and a target but also by their locations. The role of a site in the first passage processes is quantified by the random walk centrality. It turns out that the site of highest random walk centrality, dubbed as a hub, intervenes in first passage processes. We show that the MFPT from a departure site to a target site is determined by a competition between direct paths and indirect paths detouring via the hub. Consequently, the MFPT displays a crossover scaling between a short distance regime, where direct paths are dominant, and a long distance regime, where indirect paths are dominant. The two regimes are characterized by power laws with different scaling exponents. The crossover scaling behavior is confirmed by extensive numerical calculations of the MFPTs on the critical percolation cluster in two dimensional square lattices.

Original languageEnglish
Article number227101
JournalPhysical Review Letters
Issue number22
StatePublished - 1 Dec 2023


Dive into the research topics of 'Heterogeneous Mean First-Passage Time Scaling in Fractal Media'. Together they form a unique fingerprint.

Cite this