In this paper, we prove that the Paley graph conjecture implies that the Paley matrix has restricted isometry property (RIP) beating the square-root bottleneck for the sparsity level. Moreover, we show that the RIP of the Paley matrix implies an improved bound on the size of transitive subtournaments in the Paley tournament.

中文翻译：

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关于Paley矩阵的受限等距性质

在本文中，我们证明了 Paley 图猜想意味着 Paley 矩阵具有限制等距属性 (RIP)，从而克服了稀疏级别的平方根瓶颈。此外，我们表明 Paley 矩阵的 RIP 意味着对 Paley 锦标赛中传递子锦标赛大小的改进限制。