Abstract
Random walks are simulated on finite stages of construction of Sierpinski carpets and it is shown that the mean number of distinct visited sites 〈 S N 〉 by N-step walks obeys finite-size scalling. The relation 〈S N〉 ∼ N D F D w ( In N) α is proved to hold in the fractal limit, where D F and D w are the fractal and the random walk dimensions, respectively, and α is a positive exponent. This confirms the Alexander-Orbach scaling relation D s = 2D F D w . We discuss the origin of the logarithmic correction and the dependence of α on D F, the lacunarity and the ramification of the fractals.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
