Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometrics

Conference item

We examine a class of fractal graphs which arise from a subclass of finitely ramified fractals. The two-sided heat kernel estimates for these graphs are obtained in terms of an effective resistance metric and they are best possible up to constants. If the graph has symmetry, these estimates can be expressed as the usual Gaussian or sub-Gaussian estimates. However, without symmetry, the off-diagonal terms show different decay in different directions. We also discuss the stability of the sub-Gaussian heat kernel estimates under rough isometrics.

Authors: Hambly, B; Kumagai, T

• Publication status: Published
• Journal: FRACTAL GEOMETRY AND APPLICATIONS: A JUBILEE OF BENOIT MANDELBROT - MULTIFRACTALS, PROBABILITY AND STATISTICAL MECHANICS, APPLICATIONS, PT 2
• Volume: 72
• Pages: 233-259
• Publication date: 2004-01-01
• Event title: Conference on Fractal Geometry and Applications - A Jubilee of Benoit Mandelbrot held at the Annual Meeting of the American-Mathematical-Society
• ISSN: 0082-0717
• ISBN: 0821836382
• Keywords: Poincare inequality; parabolic Harnack inequality; random walks on graphs; anomalous diffusion; rough isometry; sub-Gaussian heat kernel bounds