﻿ DZLIU

# Dang-Zheng Liu

Office:
Room 1520
Management and Research Building
East Campus, University of Science and Technology of China
Hefei, Anhui, 230026 China
Email: dzliu at ustc dot edu dot cn

## Biography

Dang-Zheng Liu received his Ph.D. degree in Mathematics from Peking University, Beijing, under the supervision of Prof. Zheng-Dong Wang. Before that, he got his Bachelor degree in Mathematics from Shannxi Normal University in 2005. From October 2010 to August 2012, he was a postdoctor in University of Talca, Chile. He joined the School of Mathematical Sciences first as a tenure-track associate professor in September 2012 and then as an associate professor in February 2016.

## Research

His research interests are Random Matrix Theory and related applications.

#### 正在研究的问题：

A. β-系综的关联函数和特征多项式。 从统计物理的观点看，Dyson指标β从β=1, 2, 4的正交、酉、辛随机矩阵系综过渡到任意正数的 β-系综是很自然的一步，而且典型的β-系综可实现为三对角随机矩阵模型(Dumitriu-Edelman实现)，进而和随机算子发生联系。 B. 随机矩阵乘积的奇异特征值和复特征值。从单个随机矩阵到多个随机矩阵的研究是个很困难的问题，而随机矩阵乘积可看做一个中间状态。关注的一个问题是大维随机矩阵的无穷乘积Lyapunov指数的统计性质。 C. 随机块状与带状矩阵。带状矩阵可以看做从随机Schrodinger算子到随机矩阵的插值，当带宽在某个临界值附近时会出现Anderson相变，这是一个重要但非常困难的问题。

## Teaching

• 09/2013~01/2014: Probability Theory
• 02/2014~06/2014: Probability Theory
• 09/2014~01/2015: Probability Theory
• 02/2015~06/2015: Probability Theory
• 09/2015~01/2016: Probability Theory
• 02/2016~06/2016: Probability Theory, Stochastic Analysis (With Elton P Hsu, Ran Wang)
• 09/2017~01/2018: Advanced Probability Theory try
• 02/2018~06/2018: Stochastic Process

## Selected Publications

 Some universal properties for restricted trace Gaussian orthogonal, unitary and symplectic ensembles   Liu, D.-Z., Zhou, D.-S.   J. Stat. Phys. 140: 268--288, 2010. paper Limit Distribution of Eigenvalues for Random Hankel and Toeplitz Band Matrices   Liu, D.-Z., Wang, Z.-D.   J. Theoret. Probab.24 (4), 988--1001, 2011. paper Local statistical properties of Schmidt eigenvalues of bipartite entanglement for a random pure state   Liu, D.-Z., Zhou, D.-S.   Int. Math. Res. Notices 2011 (4):725--766, 2011. paper On Explicit Probability Densities Associated with Fuss-Catalan Numbers   Liu, D.-Z., Song, C., Wang, Z.-D.   Proc. Amer. Math. Soc. 139, 3735--3738, 2011. paper Fluctuations of Eigenvalues for Random Toeplitz and Related Matrices   Liu, D.-Z., Sun, X., Wang, Z.-D.   Electron. J. Probab. 17, no. 95, 1--22, 2012. paper Asymptotics for products of characteristic polynomials in classical β-ensembles   Desrosiers, P., Liu, D.-Z.   Constructive Approximation 39, no. 2, 273-322, 2014.paper Scaling Limits of Correlations of Characteristic Polynomials for the Gaussian β-Ensemble with External Source   Desrosiers, P., Liu, D.-Z.   Int. Math. Res. Notices, Vol. 2015, No. 12, 3751–3781, 2015. paper Raney distributions and random matrix theory   Forrester, P.J., Liu, D.-Z.   J. Stat. Phys. 158, no.5, 1051-1082, 2015. paper Selberg integrals, super-hypergeometric functions and applications to β-ensembles of random matrices   Desrosiers, P., Liu, D.-Z.   Random Matrices Theory Appl. 4, no.2, 1550007, 59pp, 2015. Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition   Forrester, P.J., Liu, D.-Z.   Communications in Mathematical Physics, vol.344, no.1, 333-368, 2016.paper Universality for products of random matrices I: Ginibre and truncated unitary cases   Liu, D.-Z., Wang, Y.   Int. Math. Res. Notices, vol. 2016, no.7, 3473-3524, 2016. paper Bulk and soft-edge universality for singular values of products of Ginibre random matrices   Liu, D.-Z., Wang, D., Zhang, L.   Annales de l'Institut Henri Poincare (B) Probabilités et Statistiques, vol.52, no.4, 1734-1762, 2016. paper Singular values for products of two coupled random matrices: hard edge phase transition   Liu, D.-Z.   Constructive Approximation, 42 pages, online doi:10.1007/s00365-017-9389-z. paper Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles   Akemann, G, Checinski, T, Liu, D.-Z., Strahov, E.   To appear in AIHP Probabilite et Statistique paper Matrix product ensembles of Hermite type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral   Forrester, P.J., Ipsen, J. R., Liu, D.-Z.   Ann. Henri Poincare, 42 pages paper

## Students

• Tiantian Chen , 9/2016 - ;
• Shuang Li , 9/2016 - ;
• Yu Xiang , 9/2016 - ;
• Lu Zhang , 9/2017 - ;

## Workshop

Workshop on Stochastic Analysis and Random Matrices, 8-10 December, 2017. Place: School of Mathematical Sciences, USTC, Hefei. Organizers: Xiang-Dong Li (Institute of Applied Mathematics, AMSS, CAS), Dang-Zheng Liu (School of Mathematical Sciences, USTC) SARM

## Mini-Courses

Random matrix theory and log-correlated Gaussian fields, NJ Simm, 26-26 March, 2018. Place: School of Mathematical Sciences, USTC, Hefei. SARM