DEPARTMENT OF MATHEMATICAL SCIENCES
Analysis and PDE Seminar Series
University of Connecticut
Diffusion processes on generalized diamond fractals
ABSTRACT: In this talk we introduce (in some sense natural) diffusion processes on a parametric family of fractals called generalized diamond fractals. These spaces arise as scaling limits of diamond hierarchical lattices, which are studied in the physics literature in relation to random polymers, Ising and Potts models among others.
In the case of constant parameters, the self-similarity of the space can be exploited to obtain a canonical Dirichlet form and a diffusion process. This approach was taken in earlier investigations due to Hambly and Kumagai to study the properties of the diffusion process and its associated heat kernel.Alternatively, a diamond fractal can also be regarded as an inverse limit of metric measure graphs. This approach allows to construct a canonical diffusion process for more general parameters through a procedure proposed by Barlow and Evans. In addition, it turns out that it is possible to give a rather explicit expression of the associated heat kernel, which is in particular uniformly continuous and admits an analytic continuation.
Thursday, November 29, 2018
Salisbury Labs 104