Covers, Laplacians, and Growth on Graphs
From CanisiusmathWiki
Covers, Laplacians, and Growth on Graphs was a project directed by Dr. Stratos Prassidis in Summer 2005.
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Poster Abstract
Covers, Laplacians, and Kestens Theorem
Tricia E Profic (Canisius College) Jack Wessel (SUNY-Binghamton)
Abstract of Poster: Kestens Theorem is a classical result that estimates the spectral radius of regular random walks on graphs. It also characterizes the two extremes in the estimate: the lowest value is obtained by regular trees and the highest by amenable graphs. We provide a proof of Kestens Theorem using combinatorial covers and normalized Laplacians. In the process, we analyze the heat kernel of the weighted ray and the dynamical properties of amenable graphs.
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Articles related to this project
- Cyclic vs Dihedral Groups
- Determinant of Laplacian via Chebyshev
- Covers and Eigenvalues
- Density of the Spectrum
- Coverings of a Systematically Weighted Path
- Amenability Equivalencies
- Universal Cover
- Covering Lemma
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