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arXiv · 1811.00113

Kesten-McKay law for the Markoff surface mod p

Matthew de Courcy-Ireland·Michael Magee
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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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Matthew de Courcy-Ireland, Michael Magee. 2018-10-31. Kesten-McKay law for the Markoff surface mod p. https://arxiv.org/abs/1811.00113

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