Volume 4 (2021)
de Courcy-Ireland, Matthew;  Magee, Michael
Kesten–McKay law for the Markoff surface mod p
Annales Henri Lebesgue, Volume 4 (2021), pp. 227-250.

Metadata

DOI10.5802/ahl.71
Keywords Markoff surface, Kesten–McKay law, cubic surfaces, graphs and groups

Abstract

For each prime p, we study the eigenvalues of a 3-regular graph on roughly p 2 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.


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