 

A. V. Dryakhlov and A. A. Tempelman
On Hausdorff Dimension of Random Fractals


Published: 
September 17, 2001 
Keywords: 
Hausdorff dimension, Random construction, Martingale 
Subject: 
Primary 54H20, 60B05; Secondary 28C10 


Abstract
We study random recursive constructions with finite "memory" in
complete metric spaces and the Hausdorff dimension of the generated
random fractals. With each such construction and any positive number
β we associate a linear operator V^{(β)} in a finite
dimensional space. We prove that under some conditions on the random
construction the Hausdorff dimension of the fractal coincides with the
value of the parameter β for which the spectral radius of
V^{(β)} equals 1.


Author information
A. V. Dryakhlov:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
axd238@psu.edu
A. A. Tempelman:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
arkady@stat.psu.edu
http://www.stat.psu.edu/~arkady/

