Exact Computation and Approximation of Stochastic and Analytic Parameters of Generalized Sierpinski Gaskets

Uta Freiberg () and Christoph Thäle ()
Additional contact information
Uta Freiberg: University of Siegen
Christoph Thäle: University of Fribourg

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 3, 485-509

Abstract: Abstract The interplay of fractal geometry, analysis and stochastics on the one-parameter sequence of self-similar generalized Sierpinski gaskets is studied. An improved algorithm for the exact computation of mean crossing times through the generating graphs SG(m) of generalized Sierpinski gaskets sg(m) for m up to 37 is presented and numerical approximations up to m = 100 are shown. Moreover, an alternative method for the approximation of the mean crossing times, the walk and the spectral dimensions of these fractal sets based on quasi-random so-called rotor walks is developed, confidence bounds are calculated and numerical results are shown and compared with exact values (if available) and with known asymptotic formulas.

Keywords: Crossing time; Einstein relation; Fractal geometry; Hausdorff dimension; Rotor walks; Sierpinski gasket; Spectral dimension; Walk dimension; 28A80; 60J10; 65C50; 05C81 (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-011-9254-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9254-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-011-9254-7

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().