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Creators/Authors contains: "Department of Mathematics, Harvard University"

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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. ; (, Bulletin of the London Mathematical Society)
  3. ; ; ; (, Bulletin of the London Mathematical Society)
    Abstract The elementary method of Balog and Ruzsa and the large sieve of Linnik are utilized to investigate the behaviour of the norm of an exponential sum over the primes. A new proof of a lower bound due to Vaughan for the norm of an exponential sum formed with the von Mangoldt function is furnished. 
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  4. ; (, Journal of Mathematical Physics)