Universality in random matrices
Local and global universality of random matrix cokernels (with Melanie Matchett Wood, submitted). | |
Universality for cokernels of random matrix products (with Roger Van Peski, submitted). | |
Some new results in random matrices over finite fields (with Kyle Luh and Sean Meehan, Journal of the London Mathematical Society, Volume 103, Issue 4 (2021), 1209-1252). | |
Random integral matrices: universality of surjectivity and the cokernel (with Melanie Matchett Wood, to appear, Inventiones Mathematicae). | |
Random matrices: overcrowding estimates for the spectrum (Journal of Functional Analysis, (2018) Volume 275, Issue 8, 2197-2224). | |
Normal vector of a random hyperplane (with Van Vu, International Mathematics Research Notices, (2018) Issue 6, 1754-1778). | |
Random matrices: tail bounds for gaps between eigenvalues (with Terence Tao and Van Vu, Probability Theory and Related Fields, (2017), Vol. 167, 3, 777-816). | |
The elliptic law (with Sean O'Rourke, International Mathematics Research Notices (2015), Vol. 2015, 7620-7689). | |
On the concentration of random multilinear forms and the universality of random block matrices (with Sean O'Rourke, Probability Theory and Related Fields (2015), Vol. 162, 1, 97-154). | |
Random doubly stochastic matrices: the circular law (Annals of Probability (2014), Vol. 42, No. 3, 1161-1196). | |
Random matrices: law of the determinant (with Van Vu, Annals of Probability (2014), Vol. 42, No. 1, 146-167). | |
Cokernels of adjacency matrices of random r-regular graphs (with Melanie Matchett Wood, preprint). | |
Universality in random polynomials
Central Limit Theorem for the number of real roots of random orthogonal polynomials
(with Yen Do, Oanh Nguyen, and Igor Pritsker, submitted). | |
Universality of Poisson limits for moduli of roots of Kac polynomials
(with Nicholas Cook, Oren Yakir, and Ofer Zeitouni, submitted). | |
Concentration of the number of intersections of random eigenfunctions on flat tori (submitted). | |
Exponential concentration for the number of roots of random trigonometric polynomials (with Ofer Zeitouni, submitted). | |
Random trigonometric polynomials: universality and non-universality of the variance for the number of real roots (with Yen Do and Oanh Nguyen, to appear, Annales de l’Institut Henri Poincare). | |
Universality of the minimum modulus for random trigonometric polynomials (with Nicholas Cook, Discrete Analysis, 20 (2021), 45pp). | |
Random eigenfunctions on flat tori: universality for the number of intersections (with Mei-Chu Chang, Oanh Nguyen, and Van Vu, International Mathematics Research Notices, (2020) Vol. 2020, Issue 24, Pages 9933-9973). | |
On the number of real roots of random polynomials (with Oanh Nguyen and Van Vu, Communications in Contemporary Mathematics (2016) Vol. 18, 4, 1550052). | |
Real roots of random polynomials: expectation and repulsion (with Yen Do and Van Vu, Proceedings London Mathematical Society (2015), Vol. 111 (6), 1231-1260). | |
Structure in large sumsets
A characterization of incomplete sequences in Fpd (with Van Vu, Journal of Combinatorial Theory, Series A, 119 (2012)). | |
Squares in sumsets (with Van Vu, on the occasion of Endre Szemeredi's 70th birthday , Bolyai Society Mathematical Studies, Vol. 21 (2010)). | |
A classification theorems for sumsets modulo a prime (with Van Vu, Journal of Combinatorial Theory, Series A, 16 (2009)). | |
Subset sums in Fp (with Endre Szemeredi and Van Vu, Acta Arithmetica, 131 (2008), 303-316). |
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Others
Rank of near uniform matrices
(with Charles Koenig, submitted). | |
Surjectivity of near square random matrices
(with Elliot Paquette, Combinatorics, Probability and Computing, 29 (2020), no. 2, 267-292). | |
Eigenvectors of random matrices of symmetric entry distributions (with Sean Meehan, Proceedings of the American Mathematical Society, (2019) Volume 147, Number 2, 835-847). | |
Concentration of distances in Wigner matrices (Linear Algebra and its Applications 536 (2018), 52-86). | |
Asymptotic Lyapunov exponents for large random matrices (Annals of Applied Probability (2017), Vol. 27, No. 6, 3672-3705). | |
A general law of large permanent (with Jozsef Balogh, Discrete and Continuous Dynamical Systems (Series A), Vol. 37, no. 10, (2017)). | |
Near invariance of the hypercube (with Scott Aaronson, Israel Journal of Mathematics (2016) 212, 385-417). | |
On a condition number of random polynomial systems (Mathematics of Computation (2016) 85, 737-757). | |
A new approach to an old problem of Erdos and Moser (Journal of Combinatorial Theory, Series A 119 (2012) 977-993). | |
On the distribution of 3-AP in sparse subsets of Fpn (Combinatorics, Probability and Computing 20 (2011), 777-791). | |
On two-point configurations in a random set (Integers 9 (2009), A3, 41-45). | |
Summer research for undergraduate students
The Rank of the Sandpile Group of Random Directed Bipartite Graphs (Atal Bhargava, Jack DePascale, Jake Koenig). | |