A Markov Chain Algorithm for determining Crossing Times through nested Graphs

Abstract

According to the by now established theory developed in order to define a Laplacian or ― equivalently ― a Brownian motion on a nested fractal, one has to solve certain renormalization problems. In this paper, we present a Markov chain algorithm solving the problem for certain classes of simple fractals $K$ provided that there exists a unique Brownian motion and hence, a unique Laplacian on $K$.

Keywords

• (nested) fractal
• self―similarity
• walk dimension
• crossing time
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-ds] mathematics [math]/dynamical systems [math.ds]
• [math.math-co] mathematics [math]/combinatorics [math.co]