Spectra of three-peg Hanoi towers graphs

2021/07/06 by Hungar, Brett, Mograby, Gamal, Phelps, Madison +2
#05C50 (Primary) 05C25 #20E80 #28A80 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.02697

Abstract

We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on fractals. By establishing a spectral decimation map between these sequences we give an elementary calculation of the spectrum of the former, which was first computed by Grigorchuk and Šunić. Our method also gives a full description of the eigenfunctions.

Related

• Schreier spectrum of the Hanoi Towers group on three pegs
• Green functions on self-similar graphs and bounds for the spectrum of the Laplacian
• Self-similar groups and holomorphic dynamics: Renormalization, integrability, and spectrum
• Spectrum of Laplacians for Graphs with Self-Loops
• Spectral Decimation for Families of Self-Similar Symmetric Laplacians on the Sierpinski Gasket