2018/10/31 by Matthew de Courcy-Ireland, de Courcy-Ireland, Matthew, Michael Magee +1
Mathematics · Computer Science · #Geometric and Algebraic Topology #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1811.00113
For each prime p, we study the eigenvalues of a 3-regular graph on roughly p2 vertices constructed from the Markoff surface. We show they asymptotically follow the Kesten-McKay law, which also describes the eigenvalues of a random regular graph. The proof is based on the method of moments and takes advantage of a natural group action on the Markoff surface.