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  1. ; (, Communications on Pure and Applied Mathematics)
    Abstract Consider the normalized adjacency matrices of randomd‐regular graphs onNvertices 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 inN, that is, . (ii) All eigenvectors of randomd‐regular graphs are completely delocalized. 
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  2. ; ; (, Communications in Mathematical Physics)
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