Nicholas A Cook
Assistant Professor of Mathematics
Current Research Interests
Highdimensional probability: random matrix theory, random graph theory, large deviations theory. Related topics in combinatorics, functional analysis, partial differential equations, number theory and mathematical physics; applications in numerical analysis and data science.
Current Appointments & Affiliations
 Assistant Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020
Contact Information
 120 Science Drive, Durham, NC 27708
 (919) 6602800
 #Website
 Google scholar profile
 arXiv page
 Background

Education, Training, & Certifications
 Ph.D., University of California  Los Angeles 2016

Previous Appointments & Affiliations
 Scholar in Residence of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020

Academic Positions Outside Duke
 Research Member, Mathematical Sciences Research Institute. 2021
 NSF Postdoctoral Scholar, Stanford University. 2019
 Stein Fellow, Stanford University. 2019  2020
 NSF Assistant Adjunct Professor, University of California, Los Angeles. 2017  2018
 NSF Postdoctoral Scholar, Stanford University. 2016  2017
 Recognition

Awards & Honors
 Expertise

Subject Headings
 Research

Selected Grants
 RTG: Training Tomorrow's Workforce in Analysis and Applications awarded by National Science Foundation 2021  2026
 Large Deviations and Extremes for Random Matrices, Tensors, and Fields awarded by National Science Foundation 2022  2025

Fellowships, Supported Research, & Other Grants
 Stein Fellowship awarded by Department of Statistics, Stanford University 2019  2020
 NSF Postdoctoral Research Fellowship awarded by National Science Foundation 2016  2019

External Relationships
 F. HoffmannLa Roche Ltd
 Publications & Artistic Works

Selected Publications

Academic Articles

Cook, N. A., et al. “Universality of Poisson Limits for Moduli of Roots of Kac Polynomials.” International Mathematics Research Notices, vol. 2023, no. 8, Apr. 2023, pp. 6648–90. Scopus, doi:10.1093/imrn/rnac021.Full Text

Cook, N., et al. “NonHermitian Random Matrices with a Variance Profile (II): Properties and Examples.” Journal of Theoretical Probability, vol. 35, no. 4, Dec. 2022, pp. 2343–82. Scopus, doi:10.1007/s10959021011402.Full Text

Cook, N. A., et al. “Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices.” Annales De L’Institut Henri Poincare (B) Probability and Statistics, vol. 58, no. 4, Nov. 2022, pp. 2284–320. Scopus, doi:10.1214/21AIHP1225.Full Text

Cook, Nicholas A., et al. Universality of Poisson limits for moduli of roots of Kac polynomials. May 2021.Link to Item

Cook, Nicholas A., et al. Regularity method and large deviation principles for the ErdősRényi hypergraph. Feb. 2021.Link to Item

Cook, Nicholas A., and Hoi H. Nguyen. Universality of the minimum modulus for random trigonometric polynomials. Jan. 2021.Link to Item

Cook, N. A., and H. H. Nguyen. “Universality of the minimum modulus for random trigonometric polynomials.” Discrete Analysis, vol. 2021, Jan. 2021. Scopus, doi:10.19086/da.28985.Full Text

Cook, N., and A. Dembo. “Large deviations of subgraph counts for sparse Erdős–Rényi graphs.” Advances in Mathematics, vol. 373, Oct. 2020. Scopus, doi:10.1016/j.aim.2020.107289.Full Text

Cook, N., and O. Zeitouni. “Maximum of the Characteristic Polynomial for a Random Permutation Matrix.” Communications on Pure and Applied Mathematics, vol. 73, no. 8, Aug. 2020, pp. 1660–731. Scopus, doi:10.1002/cpa.21899.Full Text

Cook, N. “The Circular Law for random regular digraphs.” Annales De L’Institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 4, Jan. 2019, pp. 2111–67. Scopus, doi:10.1214/18AIHP943.Full Text

Cook, N. “Lower bounds for the smallest singular value of structured random matrices.” Annals of Probability, vol. 46, no. 6, Nov. 2018, pp. 3442–500. Scopus, doi:10.1214/17AOP1251.Full Text

Basak, A., et al. “Circular law for the sum of random permutation matrices.” Electronic Journal of Probability, vol. 23, Jan. 2018. Scopus, doi:10.1214/18EJP162.Full Text

Cook, N., et al. “Nonhermitian random matrices with a variance profile (I): Deterministic equivalents and limiting ESDs.” Electronic Journal of Probability, vol. 23, Jan. 2018. Scopus, doi:10.1214/18EJP230.Full Text

Cook, Nicholas, et al. “Size biased couplings and the spectral gap for random regular graphs.” The Annals of Probability, vol. 46, no. 1, Institute of Mathematical Statistics, Jan. 2018. Crossref, doi:10.1214/17aop1180.Full Text

Cook, N. “The circular law for random regular digraphs with random edge weights.” Random Matrices: Theory and Application, vol. 6, no. 3, July 2017. Scopus, doi:10.1142/S2010326317500125.Full Text

Cook, N. A. “On the singularity of adjacency matrices for random regular digraphs.” Probability Theory and Related Fields, vol. 167, no. 1–2, Feb. 2017, pp. 143–200. Scopus, doi:10.1007/s0044001506798.Full Text

Cook, N. A. “Discrepancy properties for random regular digraphs.” Random Structures and Algorithms, vol. 50, no. 1, Jan. 2017, pp. 23–58. Scopus, doi:10.1002/rsa.20643.Full Text

Cook, Nicholas A., et al. NonHermitian random matrices with a variance profile (I): Deterministic equivalents and limiting ESDs. Dec. 2016.Link to Item

Cook, Nicholas A. Dense random regular digraphs: singularity of the adjacency matrix. Mar. 2014.Link to Item

Cook, Nicholas A., et al. “Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices (Accepted).” To Appear in Annales De L’Institut Henri Poincaré (B) Probabilités Et Statistiques.Link to Item


Preprints

Cook, Nicholas A., et al. Full large deviation principles for the largest eigenvalue of subGaussian Wigner matrices. 28 Feb. 2023.Link to Item

Cook, Nicholas A., and Amir Dembo. Typical structure of sparse exponential random graph models. 12 Aug. 2022.Link to Item


 Teaching & Mentoring

Recent Courses
 MATH 340: Advanced Introduction to Probability 2023
 MATH 641: Probability 2023
 MATH 740: Advanced Introduction to Probability 2023
 STA 231: Advanced Introduction to Probability 2023
 MATH 340: Advanced Introduction to Probability 2022
 MATH 740: Advanced Introduction to Probability 2022
 MATH 79090: Minicourse in Advanced Topics 2022
 STA 231: Advanced Introduction to Probability 2022
 MATH 641: Probability 2021

Advising & Mentoring

Haotian Gu, PhD, Duke, 2021present
Mentored 3 Duke undergraduate students in a DOMath research project on "Structure and stability for Brascamp–Lieb inequalities", Summer 2022.
Pengda Liu, undergraduate honors thesis, Stanford, 20192020.

Haotian Gu, PhD, Duke, 2021present

Teaching Activities

In Summer 2022 I gave a 5lecture course on "Geometric Methods in Random Matrix Theory" at the University of Michigan Random Matrix Theory Summer School
.
In Summer 2022 I led a project for the Duke math department's DoMath summer undergraduate research program.

In Summer 2022 I gave a 5lecture course on "Geometric Methods in Random Matrix Theory" at the University of Michigan Random Matrix Theory Summer School
.
 Scholarly, Clinical, & Service Activities

Presentations & Appearances
 Structure and stability for sparse exponential random graphs. Conference on Random Matrix Theory and Numerical Linear Algebra. June 24, 2022 2022
 Geometric Methods in Random Matrix Theory. Random Matrix Theory Summer School. June 2022 2022
 Structure and stability for sparse exponential random graphs. Southeastern Probability Conference (SEPC). May 2022 2022
 Structure and stability for sparse exponential random graphs. Probability Seminar. Cornell University Math Dept.. April 2022 2022
 Structure and stability for sparse exponential random graphs. Probability Seminar. Lehigh, Northwestern, UMN. April 2022 2022
 Large deviations and the regularity method for sparse random hypergraphs. Probability Seminar. Centre de recherches mathématiques. December 1, 2021 2021
 Universalidad en los extremos de polinomios aleatorios (in Spanish). Seminario de Probabilidad Hispanohablante. November 22, 2021 2021
 Large deviations and regularity method for sparse random hypergraphs. Probability and Combinatorics Seminar. Ohio State University. October 7, 2021 2021
 Large deviations and regularity method for sparse random hypergraphs. Probability Seminar. MIT. October 4, 2021 2021
 Large deviations and the regularity method for the Erdős–Rényi (hyper)graph. Probability Seminar. University of California, Berkeley. September 29, 2021 2021
 Large deviations and the regularity method for the Erdős–Rényi (hyper)graph. One World Probability Seminar. June 17, 2021 2021
 Regularity method and large deviation principles for the Erdős–Rényi hypergraph. Combinatorics seminar. University of Warwick. June 11, 2021 2021
 Universality for the minmodulus of random trigonometric polynomials. Probability Seminar. University of Chicago. April 2, 2021 2021
 Universality for the minimum modulus of random trigonometric polynomials. Probability and Analysis Webinar. March 1, 2021 2021
 Universality for the minimum modulus of random trigonometric polynomials. Probability Seminar. City University of New York. February 23, 2021 2021
 Universality for the minimum modulus of random trigonometric polynomials. Probability Seminar. University of Southern California. February 19, 2021 2021
 Universality for the minimum modulus of random trigonometric polynomials. Probability Seminar. Duke University. February 18, 2021 2021
 Universality for the minimum modulus of random trigonometric polynomials. Probability and the City Seminar. Columbia University & Courant Institute. January 22, 2021 2021
 The minimum modulus for random trigonometric polynomials. Probability seminar. University of British Columbia. November 2020 2020
 Branching Brownian motion and the roadfield model. Probability seminar. University of California, Berkeley. May 2020 2020
 A branching Brownian motion perspective on the RoadField Model. Applied Mathematics Seminar. Stanford University. February 2020 2020
 Sparse exponential random graphs. Centre International de Rencontres Mathématiques. January 2020 2020
 Convergence to Brown’s spectral measure for polynomials in Ginibre matrices. Latin American Congress of Probability and Mathematical Statistics. December 2019 2019
 Large Deviations for Sparse Erdos–Renyi Graphs. Advances in Asymptotic Probability in Honor of Amir Dembo's 60th Birthday . December 2018 2018

Outreach & Engaged Scholarship
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