nickcook[at]math[dot]ucla[dot]edu

I am broadly interested probability, analysis, high-dimensional geometry and combinatorics. Most of my research centers on Random Matrix Theory, which intersects all of these fields, and which has applications to random graphs, mathematical physics, theoretical computer science, neuroscience and ecology.

Papers and preprints:

  • Circular law for the sum of random permutation matrices (with Anirban Basak and Ofer Zeitouni). arXiv
  • The circular law for random regular digraphs. arXiv
    Preprint.
  • Limiting spectral distribution for non-Hermitian random matrices with a variance profile (with Walid Hachem, Jamal Najim and David Renfrew). arXiv
    Preprint.
  • Lower bounds for the smallest singular value of structured random matrices. arXiv
    Annals of Probability, to appear.
  • Spectral properties of non-Hermitian random matrices. url
    PhD Thesis, UCLA.
  • Size biased couplings and the spectral gap for random regular graphs (with Larry Goldstein and Toby Johnson). arXiv
    Annals of Probability, to appear.
  • The circular law for random regular digraphs with random edge weights. arXiv
    Random Matrices: Theory Appl., 06, 1750012, 2017. doi:10.1142/S2010326317500125.
  • Discrepancy properties for random regular digraphs. arXiv
    Random Struct. Algor., 50:23–58, 2016. doi:10.1002/rsa.20643.
  • On the singularity of adjacency matrices for random regular digraphs. arXiv
    Probab. Theory Relat. Fields, 167(1):143--200, Feb 2017. doi:10.1007/s00440-015-0679-8.

Slides:

  • Circular laws for random regular digraphs. pdf
    AMS Fall Western Sectional Meeting, UC Riverside, November 2017
  • Inhomogeneous circular laws for random matrices with non-identically distributed entries. pdf
    Probability and Mathematical Physics Seminar, UC Davis, April 2017
  • Random regular digraphs: singularity and spectrum. pdf
    Probability Seminar, Stanford, November 2015

Any opinions, findings, and conclusions or recommendations expressed on this webpage are those of the author and do not necessarily reflect the views of the National Science Foundation.