Mathematical Sciences - Analysis and PDE Seminar - "Diffusion processes on generalized diamond fractals" by Patricia Alonso-Ruiz, (University of Connecticut)

Thursday, November 29, 2018
12:00 pm to 1:00 pm
Floor/Room #: 
104

DEPARTMENT OF MATHEMATICAL SCIENCES

Analysis and PDE Seminar Series

Patricia Alonso-Ruiz
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

12:00PM-1:00PM

Salisbury Labs 104