My research interests include free probability theory, random matrix theory, operator algebras, quantum information theory, applied probability, machine learning and high dimensional statistics.
My research is supported by NSF award LEAPS-MPS-2316836 (2023.08-2025.07), Simons Travel Support for Mathematicians No. 713454 (2020.09-2025.08), and NSF CAREER Award DMS-2339565 (2024.09-2029.09).
Outlier eigenvalues for full rank deformed single ring random matrices, with Ching-Wei Ho and Zhi Yin, submitted. [arXiv:2502.10796]
The Brown measure of a sum of two free random variables, one of which is R-diagonal, with Hari Bercovici, submitted. [arXiv:2209.12379]
Spectrum of Laplacian matrices associated with large random elliptic matrices, with Sean O'Rourke and Zhi Yin, to appear in Annales de l'Institut Henri Poincaré. [arXiv:2308.16171]
Brown measure of the sum of an elliptic operator and a free random variable in a finite von Neumann algebra, to appear in American Journal of Mathematics. [arXiv:2108.09844]
Deformed single ring theorems, with Ching-Wei Ho, Journal of Functional Analysis. Vol 288, Issue 5 (2025), 110797. [arXiv:2210.11147][journal]
The Brown measure of a sum of two free random variables, one of which is triangular elliptic, with Serban Belinschi and Zhi Yin, Adv. in Math. Vol. 441 (2024), 109562 [arXiv:2209.11823][journal]
Superconvergence and regularity of densities in free probability, with Hari Bercovici and Jiun-Chau Wang, Trans. Amer. Math. Soc. 376 (2023), 4901-4956 [arXiv:2010.01248][journal]
Brown Measures of Free Circular and Multiplicative Brownian Motions with Self-Adjoint and Unitary Initial Conditions, with Ching-Wei Ho, Journal of the European Mathematical Society (JEMS), Vol. 25, no. 6, 2163–2227 (2023) [arXiv:1908.08150] [journal]
Brown measure of R-diagonal operators, revisited, Chapter 10 at Operators, Semigroups, Algebras and Function Theory, Operator Theory: Advances and Applications 292, Volume from IWOTA Lancaster 2021. [arXiv:2204.01896] [book chapter]
The spectrum of local random Hamiltonians, with Benoit Collins, Zhi Yin, and Liang Zhao, to appear in J. Phys. A: Math. Theor. 56 (2023), no. 3, Paper No. 035201, 28 pp. [arXiv:2210.00855] [journal]
Superconvergence in free probability limit theorems for arbitrary triangular arrays, with with Hari Bercovici, Ching-Wei Ho, and Jiun-Chau Wang, Proceedings of AMS, 150 (2022), no. 12, 5253-5265. [arXiv:2202.02240]
Series of Free R-diagonal Random Variables, with Hari Bercovici and Alexandru Nica, Pure and Applied Functional Analysis, Vol. 7, no. 1, 41-51 (2022). [journal]
An operator that relates to semi-meander polynomials via a two-sided q-Wick formula. with Alexandru Nica, Indiana Univ. Math. J. 69, no. 6, 2089–2127 (2020). [journal]
Free-Boolean independence with amalgamation, with Weihua Liu, Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 22, No. 04, 1950028 (2019). [journal]
Continuity and growth of free multiplicative convolution semigroups, with Xiaoxue Deng, Electron. Commun. Probab. 24: 1-11 (2019). [journal]
Quasifree stochastic cocycles and quantum random walks, with ACR Belton, M Gnacik, and JM Lindsay, Journal of Statistical Physics 176 (1), 1-39 (2019). [journal]
The PPT square conjecture holds generically for some classes of independent states, with Benoit Collins and Zhi Yin, J. Phys. A: Math. Theor. 51 425301 (2018). [journal]
Superconvergence to freely infinitely divisible distributions, with Hari Bercovici and Jiun-Chau Wang, Pacific J. Math. 292, no. 2, 273–290 (2018). [journal]
On the free convolution with a free multiplicative analogue of the normal distribution. J. Theoret. Probab. 28, no. 4, 1354–1379 (2015). [journal]
Estimates for compression norms and additivity violation in quantum information, with Benoit Collins and Motohisa Fukuda, Internat. J. Math. 26, no. 1, 1550002, 20 pp (2015). [journal]
Local limit theorems for multiplicative free convolutions. with Michael Anshelevich and Jiun-Chau Wang, J. Funct. Anal. 267, no. 9, 3469–3499 (2014). [journal]
On the supports of measures in free multiplicative convolution semigroups, with HW Huang, Math. Z. 278, no. 1-2, 321–345 (2014). [journal]
Free Brownian motion and free convolution semigroups: multiplicative case. Pacific J. Math. 269, no. 1, 219–256 (2014). [journal]
On regularity for measures in multiplicative free convolution semigroups. Complex Anal. Oper. Theory 7, no. 4, 1337–1343. [journal ]
My arXiv author page is here.