Distribution of first-passage times to specific targets on compactly explored fractal structures

Yasmine Meroz, Igor M. Sokolov, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

Abstract

The distribution of the first passage times (FPT) of a one-dimensional random walker to a target site follows a power law F(t)~t-3 /2. We generalize this result to another situation pertinent to compact exploration and consider the FPT of a random walker with specific source and target points on an infinite fractal structure with spectral dimension ds<2. We show that the probability density of the first return to the origin has the form F(t)~tds/2-2, and the FPT to a specific target at distance r follows the law F(r,t)~rd w-dftds/2-2, where dw and df are the walk dimension and the fractal dimension of the structure, respectively. The distance dependence of F(r,t) reproduces the one of the mean FPT of a random walk in a confined domain.

Original languageEnglish
Article number020104
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume83
Issue number2
DOIs
StatePublished - 14 Feb 2011

Fingerprint

Dive into the research topics of 'Distribution of first-passage times to specific targets on compactly explored fractal structures'. Together they form a unique fingerprint.

Cite this