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| Melanie Pivarski |
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| Ph.D. (2006) Cornell University |
First Position
Visiting assistant professor at Texas A&M UniversityDissertation
Heat Kernels on Euclidean ComplexesAdvisor:
Laurent Saloff-Coste
Research Area:Probability
and Analysis
Abstract: In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincaré inequality for complexes with bounded geometry and use this to determine uniform small time heat kernel bounds via a theorem of Sturm. We then consider such complexes with an underlying finitely generated group structure. We use techniques of Saloff-Coste and Pittet to show a large time asymptotic equivalence for the heat kernel on the complex and the heat kernel on the group.
Last modified: August 21, 2006