Spectral properties of polynomials in independent Wigner and deterministic matrices
Spectral properties of polynomials in independent Wigner and deterministic matrices
复制标题
独立维格纳矩阵和确定性矩阵中多项式的谱特性
DOI：
10.1016/j.jfa.2017.07.010
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Capitaine
中科院分区：
文献类型：
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作者：
S. Belinschi;M. Capitaine
一方面，我们几乎可以肯定地证明，对于大维，独立维格纳矩阵和确定性矩阵中，在距一系列确定性概率测度的支持点一定距离的任何区间内，都不存在埃尔米特多项式的特征值，这是用自由概率工具计算的。另一方面，我们建立了独立维格纳矩阵和任何具有强极限分布的确定性矩阵族的强渐近自由性。
On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic probability measures, which is computed with the tools of free probability. On the other hand, we establish the strong asymptotic freeness of independent Wigner matrices and any family of deterministic matrices with strong limiting distribution.