Alexander Teplyaev
University of Connecticut
Title: Uniqueness of Brownian motion on Sierpinski carpets
Up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Therefore, for each such fractal the law of the Brownian motion is uniquely determined and the Laplacian is well defined. As a consequence, we show that the geometry of the space uniquely defines spectral and walk dimensions, which determine the behavior of the natural diffusion process. This is a joint work with Martin Barlow, Richard Bass and Takashi Kumagai.
©2010, Department of Mathematical Sciences
Last Modified: February 26, 2009