Stochastic models for diffusion in disordered media using fractals

O.D. Jones

Abstract: When viewed at an appropriate scale, a disordered medium can behave as if it is strictly less than three dimensional. As fractals typically have non-integer dimensions, they are natural models for disordered media, and diffusion on fractals can be used to model diffusion in disordered media. In particular, it can be used to obtain heat kernel bounds. In this paper we review the work in this area and describe how bounds on branching processes lead to bounds on heat kernels.

Acknowledgement: This worked was funded by the Australian Research Council.

The author:

• Owen Jones, Discipline of Mathematics, The University of Queensland. Owen.Jones@maths.anu.edu.au

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Last modified: 1st March 1996