Welcome to Zhigang Bao's HomePage


Zhigang Bao

I'm an Assistant Professor in Department of Mathematics at Hong Kong University of Science and Technology.

In general, I'm interested in Probability, Statistical Physics, and Mathematical Statistics.


Contact

Email: mazgbao@ust.hk

Address: Rm 3429, Department of Mathematics, HKUST,  Clear Water Bay, Kowloon, Hong Kong.


Opennings

Postdoc positions are available. Applicants with background in random matrix theory / high-dimensional statistics are welcome.



Teaching

MATH 2431-Honors Probability, HKUST, Spring 2020

MATH 6450C-Introduction to Random Matrix Theory, HKUST, Spring 2020


Publications

21.Spectral rigidity for addition of random matrices at the regular edge

    with L. Erdos and K. Schnelli

      Journal of Functional Analysis (to appear)

20. Singular vector and singular subspace distribution for matrix denoising model

    with X.C. Ding and K. Wang

      Annals of Statistics (to appear)

19. Tracy-Widom limit for Kendall's tau   

      Annals of Statistics, 47(6), 3504-3532, (2019)

18. On the support of the free additive convolution

    with L. Erdos and K. Schnelli

     Journal d'Analyse Mathematique (to appear) 

17. Local single ring theorem on optimal scale 

      with L. Erdos and K. Schnelli

      Annals of Probability, 47(3), 1270-1334, (2019)

16. Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case

      with J. Hu, G. M. Pan and W. Zhou  

      Annals of Statistics, 47(1), 612-640, (2019)

15. Convergence rate of spectral distribution of addition of random matrices  

      with L. Erdos and K. Schnelli 

      Advances in  Mathematics , 319, 251-291, (2017)

14. Delocalization for a class of random block band matrices 

      with L. Erdos

      Probability  Theory and Related Fields, 167(3), 673-776, (2017)

13. Test of independence for high-dimensional random vectors based on block correlation matrices

      with J. Hu, G. M. Pan and W. Zhou  

      Electronic  Journal of  Statistics, 11(1), 1527-1548, (2017)

12. Local law of addition of random matrices on optimal scale  

      with L. Erdos and K. Schnelli

      Communications in  Mathematical  Physics,  349(3), 947-990, (2017) 

11. Local stability of the free additive convolution 

     with L. Erdos and K. Schnelli

      Journal of  Functional  Analysis,  271(3), 672-719, (2016) 

10. Spectral statistics of large dimensional Spearman's rank correlation matrix and its application

      with  L.-C. Lin, G. M. Pan and W. Zhou 

       Annals of Statistics,  43(6), 2588-2623, (2015)

9. Universality for the largest eigenvalue of sample covariance matrices with general population

    with G. M. Pan and W. Zhou 

    Annals of Statistics,  43(1), 382-421, (2015)

8. The logarithmic law of random determinant   

    with G. M. Pan and W. Zhou

    Bernoulli, 21(3), 1600-1628, (2015)

7. On the MIMO channel capacity for the general channels 

    with G. M. Pan, and W. Zhou

    IEEE Transactions on  Information Theory,  61 (6), 3413-3426, (2015)

6.  CLT for linear spectral statistics of Hermitian Wigner matrices with general  moment conditions 

    with J. S. Xie  

   Theory of Probability and its  Applications,  60 (2), 311332, (2015)

5. Universality for a global property of the eigenvectors of Wigner matrices

    with G. M. Pan and W. Zhou 

    Journal of  Mathematical  Physics,  55, 023303, (2014)

4. On asymptotic expansion and CLT of linear eigenvalue statistics for sample covariance matrices when N/M\to 0           

     Theory of Probability and its  Applications, 59 (2), 313339, (2014)

3. Central limit theorem for partial linear eigenvalue statistics of random matrices

    with G. M. Pan and W. Zhou 

    Journal of  Statistical  Physics,  150, Issue 1, 88-129, (2013)

2. Tracy-Widom law for the extreme eigenvalues of sample correlation matrices 

    with G. M. Pan and W. Zhou 

    Electronic  Journal of  Probability, 17, No. 88, 1-32, (2012)

1. Local Semicircle law and Gaussian fluctuation for Hermite \beta ensemble

    with Z.G. Su  

    Scientia Sinica Mathematica , 42 (10), (2012)


Preprints

4. Central limit theorem for mesoscopic eigenvalue statistics of the free sum of matrices

    with K. Schnelli, and Y.Y. Xu 

     arXiv: 2001.07661

3. On Cramer-von Mises statistic for the spectral distribution of random matrices

    with Y.K. He 

     arXiv: 1911.04151

2. Principal components of spiked covariance matrices in the supercritical regime

    with X.C. Ding, J.M. Wang, and K. Wang 

     arXiv: 1907.12251

1. Tracy-Widom limit for Spearman's rho

    Preprint 




Grants:

(2019-2022) Hong Kong RGC GRF Grant 16301519

(2018-2021) Hong Kong RGC GRF Grant 16300618

(2017-2020) Hong Kong RGC ECS Grant 26301517 (with RGC Early Career Award)

(2017-2020) HKUST Initiation Grant IGN16SC09

(2016-) HKUST Start-up Grant 



Brief Curriculum Vitae:

Since 2016.8:     Assistant Professor at HKUST

2014-2016:        Postdoc at IST Austria, supported by ERC Advanced Grant RANMAT, No. 338804 

2013-2014:        Research Assistant at School of Physical and Mathematical Sciences, Nanyang Technological University

2011-2012:        Project Officer at School of Physical and Mathematical Sciences, Nanyang Technological University

2008-2013:        PhD,  Department of Mathematics, Zhejiang University

                                    -Advisor: Prof. Zhonggen Su

2004-2008:        B.S., Department of Mathematics, Zhejiang University