I am broadly interested probability, analysis, combinatorics and high-dimensional geometry. Most of my research falls within Random Matrix Theory, which intersects all of these fields. Random matrices also have important applications in mathematical physics, dynamical systems (neural networks and ecological food webs), number theory, and to the study of random graphs.

Papers and preprints:

  • Large deviations of subgraph counts for sparse Erdős–Rényi graphs (with Amir Dembo). arXiv
    Preprint.
  • Maximum for the characteristic polynomial of a random permutation matrix (with Ofer Zeitouni). arXiv
    Preprint.
  • Circular law for the sum of random permutation matrices (with Anirban Basak and Ofer Zeitouni). arXiv
    Electronic Journal of Probability, 23:1–51, 2018. doi:10.1214/18-EJP162
  • The circular law for random regular digraphs. arXiv
    Annales de l'Institute Henri Poincaré, Probabilités et Statistiques, to appear.
  • Non-Hermitian random matrices with a variance profile (I): Deterministic equivalents and ESDs (with Walid Hachem, Jamal Najim and David Renfrew). arXiv
    Electronic Journal of Probability, to appear.
  • Lower bounds for the smallest singular value of structured random matrices. arXiv
    Annals of Probability, 46(6):3442–3500, 2018. doi:10.1214/17-AOP1251
  • 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, 46(1):72–125, 2018. doi:10.1214/17-AOP1180
  • 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:

  • Pseudospectrum and spectral anti-concentration: Beyond mean field models. pdf
    IPAM QLA Culminating Workshop, Lake Arrowhead, CA, June 2018
  • The maximum of the characteristic polynomial for a random permutation matrix. pdf
    Random matrices and free probability workshop, IPAM, UCLA, May 2018
  • 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

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