# Yizhe Zhu

I'm a Visiting Assistant Professor at University of California, Irvine. I'm also a Postdoc in the Collaboration on the Theoretical Foundations of Deep Learning. My mentor is Roman Vershynin.

In the fall semester of 2021, I was a Postdoc Fellow at Simons Laufer Mathematical Sciences Institute (formerly MSRI) for the program Universality and Integrability in Random Matrix Theory and Interacting Particle Systems in Berkeley, California. I obtained my Ph.D. in Mathematics from the University of California, San Diego in 2021. My advisor is Ioana Dumitriu. I obtained Bachelor's degree in Mathematics and Applied Mathematics from Shanghai Jiao Tong University. My CV is here.

Email: yizhe.zhu[at]uci.edu

Office: 510V Rowland Hall

I'm organizing the Combinatorics and Probability Seminar at UCI.

Teaching

Spring 2022: MATH 3A (Introduction to Linear Algebra) and MATH 130C (Stochastic Process)

Spring 2023: MATH 130A (Probability Theory I) and MATH 130C (Stochastic Process)

Math 199 (Supervised Reading and Research) Spring 2022/2023, Winter 2023

I am actively involved in the UC Irvine Math CEO (Community Educational Outreach) high school program.

Travel

2023

June 28-30, 21st INFORMS Applied Probability Society Conference, Nancy, France

May 23-24, Collaboration on the Theoretical Foundations of Deep Learning Meeting, TTIC, Chicago.

April 25-27, Artificial Intelligence and Statistics (AISTATS) 2023, Valencia, Spain

April 22, Southern California Applied Mathematics Symposium, UCI

April 13-14, UCLA Synthetic Data workshop

Mar 27-31, Spectra of Random Graphs and Related Combinatorial Problems, Eurandom, Eindhoven, Netherlands

Feb 12-17, Information Theory and Applications Workshop, San Diego

Jan 4-7, AMS Special Session on Tensor Representation, Completion, Modeling and Analytics of Complex Data, JMM 2023, Boston

### Research Interests

I am interested in probability, combinatorics, and their applications in data science. I am working on:

Random matrices, random graphs

Random tensors, random hypergraphs

Community detection, tensor completion, neural networks, differential privacy

### Preprints

Differentially private Low-dimensional representation of high-dimensional data, with Yiyun He, Thomas Strohmer, and Roman Vershynin, submitted, 2023.

A non-backtracking method for long matrix completion, with Ludovic Stephan, 2023.

Extreme singular values of inhomogeneous sparse random rectangular matrices, with Ioana Dumitriu, submitted, 2022.

Robust recovery of low-rank matrices and low-tubal-rank tensors from noisy sketches, with Anna Ma and Dominik Stöger, submitted, 2022.

The characteristic polynomial of sums of random permutations and regular digraphs, with Simon Coste and Gaultier Lambert, submitted, 2022.

Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model, with Ioana Dumitriu and Haixiao Wang, submitted, 2021.

Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks, with Zhichao Wang, submitted, 2021.

### Papers

Spectral gap-based deterministic tensor completion, with Kameron Decker Harris, Oscar Lopez, and Angus Read, 14th International Conference on Sampling Theory and Applications (SampTA), 2023, to appear.

Algorithmically effective differentially private synthetic data, with Yiyun He and Roman Vershynin, 36th Annual Conference on Learning Theory (COLT), 2023, to appear.

Overparameterized random feature regression with nearly orthogonal data, with Zhichao Wang, Proceedings of The 26th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 206:8463-8493, 2023. [conference proceeding]

Global eigenvalue fluctuations of random biregular bipartite graphs, with Ioana Dumitriu, Random Matrices: Theory and Applications, 2023, to appear. [journal]

On the second eigenvalue of random bipartite biregular graphs, Journal of Theoretical Probability, 36, 1269–1303, 2023. [journal]

Sparse recovery properties of discrete random matrices, with Asaf Ferber, Ashwin Sah, and Mehtaab Sawhney, Combinatorics, Probability and Computing, 32(2), 316-325, 2023. [journal]

Sparse random hypergraphs: Non-backtracking spectra and community detection, with Ludovic Stephan, 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2022. [conference proceeding]

Deterministic tensor completion with hypergraph expanders, with Kameron Decker Harris, SIAM Journal on Mathematics of Data Science, 3(4), 1117-1140, 2021. [journal]

Spectra of random regular hypergraphs, with Ioana Dumitriu, The Electronic Journal of Combinatorics, 28(3), P3-36, 2021. [journal]

Sparse random tensors: Concentration, regularization and applications, with Zhixin Zhou, Electronic Journal of Statistics, 15(1), 2483-2516, 2021. [journal]

Community detection in the sparse hypergraph stochastic block model, with Soumik Pal, Random Structures and Algorithms, 59(3): 407– 463, 2021. [journal]

Asymptotic behavior of a sequence of conditional probability distributions and the canonical ensemble, with Yu-Chen Cheng and Hong Qian, Annales Henri Poincaré, 22, 1561–1627, 2021. [journal]

Eigenvalues of the non-backtracking operator detached from the bulk, with Simon Coste, Random Matrices: Theory and Applications, 10(3), 2150028, 2021. [journal]

Exact recovery in the hypergraph stochastic block model: A spectral algorithm, with Sam Cole, Linear Algebra and its Applications, 593, 45-73, 2020. [journal]

A graphon approach to limiting spectral distributions of Wigner-type matrices, Random Structures and Algorithms, 56(1), 251– 279, 2020. [journal]

Sparse general Wigner-type matrices: Local law and eigenvector delocalization, with Ioana Dumitriu, Journal of Mathematical Physics, 60(2), 023301, 2019. [journal]