Z. Bao

activity

20112026

most citedUniversality for the largest eigenvalue of sample covariance matrices with general population

101 citations · 243 across the 33 of their papers we have counts for

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Showing 2012 · math.PRShow all

3 papers · 2 filters

math.PR2012

Universality for a global property of the eigenvectors of Wigner matrices

Zhigang Bao, Guangming Pan, Wang Zhou

Let $M_{n}$ be an $n \times n$ real (resp. complex) Wigner matrix and $U_{n} Λ_{n} U_{n}^{*}$ be its spectral decomposition. Set $(y_{1}, y_{2} ..., y_{n})^{T} = U_{n}^{*} x$ , where $x = (x_{1}, x_{2}, ...,$ $x_{n})^{T}$ i…

math.PR2012★ 13 cited

The logarithmic law of random determinant

Zhigang Bao, Guangming Pan, Wang Zhou

Consider the square random matrix $A_{n} = (a_{ij})_{n, n}$ , where ${a_{ij} := a_{ij}^{(n)}, i, j = 1, \dots, n}$ is a collection of independent real random variables with means zero and var…

math.PR2012★ 20 cited

Central limit theorem for partial linear eigenvalue statistics of Wigner matrices

Zhigang Bao, Guangming Pan, Wang Zhou

In this paper, we study the complex Wigner matrices $M_{n} = \frac{1}{n} W_{n}$ whose eigenvalues are typically in the interval $[- 2, 2]$ . Let $λ_{1} \leq λ_{2} ... \leq λ_{n}$ be the ordered…