Consider the normalized adjacency matrices of random d-regular graphs on N vertices with fixed degree . We prove that, with probability for any , the following two properties hold as provided that : (i) The eigenvalues are close to the classical eigenvalue locations given by the Kesten–McKay distribution. In particular, the extremal eigenvalues are concentrated with polynomial error bound in N, that is, . (ii) All eigenvectors of random d-regular graphs are completely delocalized.

中文翻译：

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直到边缘的随机 d-正则图的谱

考虑具有固定度数的N 个顶点上的随机d -正则图的归一化邻接矩阵。我们证明，以概率对于任何，以下两个性质成立前提是： (i) 特征值接近 Kesten-McKay 分布给出的经典特征值位置。特别是，极值特征值集中在N中的多项式误差范围内，即。(ii) 随机d正则图的所有特征向量完全离域。