# 刘党政

E-Mail：dzliu AT ustc.edu.cn

2001-2005，陕西师范大学数学与信息科学澳门新葡新京官方网站，本科生

2005-2010, 北京大学澳门新葡新京，博士生

A. 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。 B. 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。C. 随机矩阵与表示论和L函数有关的课题是很吸引我的课题，正在学习中

[1] Desrosiers, P., Liu, D.-Z.， Asymptotics for products of characteristic polynomials in classical β-ensembles，

Constructive Approximation 39, no. 2, 273-322, 2014

[2] Desrosiers, P., Liu, D.-Z.，Scaling Limits of Correlations of Characteristic Polynomials for the Gaussian β-Ensemble with External Source, Int. Math. Res. Notices, Vol. 2015, No. 12, 3751–3781, 2015.

[3] Forrester, P.J., Liu, D.-Z.,Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition, Communications in Mathematical Physics, vol.344, no.1, 333-368, 2016.

[4] Liu, D.-Z., Wang, Y., Universality for products of random matrices

I: Ginibre and truncated unitary cases,Int. Math. Res. Notices, vol. 2016, no.7, 3473-3524, 2016.

[5] Liu, D.-Z., Wang, D., Zhang, L.,

Bulk and soft-edge universality for singular values of products of Ginibre random matrices

Annales de l'Institut Henri Poincare (B) Probabilités et Statistiques, vol.52, no.4, 1734-1762, 2016.

[6] Akemann, G, Checinski, T, Liu, D.-Z., Strahov, E., Finite rank perturbations in products of coupled

random matrices: From one correlated to two Wishart ensembles, AIHP(B) Probabilite et Statistique, Vol. 55, No. 1, 441–479, 2019