Kesten-McKay law for random subensembles of Paley equiangular tight frames

Dustin G. Mixon; Hans Parshall; Mark Magsino

Kesten-McKay law for random subensembles of Paley equiangular tight frames

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arxiv 1905.04360 v1 pith:OVUCW7QY submitted 2019-05-10 cs.IT math.COmath.ITmath.PR

Kesten-McKay law for random subensembles of Paley equiangular tight frames

Mark Magsino , Dustin G. Mixon , Hans Parshall This is my paper

classification cs.IT math.COmath.ITmath.PR

keywords equiangularframestightpaleyrandomredundancysubensemblesanalysis

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We apply the method of moments to prove a recent conjecture of Haikin, Zamir and Gavish (2017) concerning the distribution of the singular values of random subensembles of Paley equiangular tight frames. Our analysis applies more generally to real equiangular tight frames of redundancy 2, and we suspect similar ideas will eventually produce more general results for arbitrary choices of redundancy.

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Linear programming bounds for cliques in Paley graphs
math.CO 2019-07 unverdicted novelty 6.0

A linear programming bound obtained by restricting the Lovász theta number to local graphs of Paley graphs rivals the Hanson-Petridis closed-form bound and is conjectured to improve on it for infinitely many cases.