Hermitian随机矩阵特征值

Eigenvalues of the Hermitian Random Matrices

利用随机矩阵理论中的矩方法研究一类Hermitian随机矩阵极端特征值的极限性质.结果表明,Hermitian随机矩阵的极端特征值几乎处处有界;特别地,对任意固定整数m,有limn→∞infλ_m(1/n^(1/2))H_n≥2σ,limn→∞supλ_(n-m)(1/^(1/2)H_n)≤-2σ,其中σ~2=mink,lσ~2_(kl).

Using the moment methods of the random matrix theory,we studied the limit properties of extreme eigenvalues of a class of Hermitian random matrices.The result shows that the extreme eigenvalue of the Hermitian random matrices Hnis bounded almost everywhere,especially for any fixed integer m,limn→∞infλm（1/n1/2）Hn≥2σ,limn→∞supλn-m（1/1/2Hn）≤-2σ,where σ2=mink,lσ2kl.