I am broadly interested probability theory and related areas of analysis, combinatorics and high-dimensional geometry. I am particularly interested in universality phenomena for high-dimensional structures such as random matrices and random graphs, and related topics in graph theory, mathematical physics and statistics.

See also my arXiv page and Google Scholar citations.

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:paper no. 33, 51 pp., 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, 23:paper no. 110, 61 pp., 2018. doi:10.1214/18-EJP230
  • 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:

  • Large deviations of subgraph counts for sparse random graphs. pdf
    Amir Dembo’s 60th birthday conference, Stanford, Dec 2018
  • 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, Nov 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, Nov 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.