4.2.2 Asymptotic Spectral Distributions for Square Matrix Theorem 4.2.2.Let H be an N X N complex random matrix whose entries a are independent random variables with identical mean, variance 1/N and finite kth moments for k 4.Then,the asymptotic spectrum of H converges almost surely to the circular law [2],namely the uniform distribution over the unit disk on the complex plane {5∈C:g≤1 whose density is given by 无（传）-1 兀 [2]V.L.Girko,Circular Law [J],Theory Prob.Appl.,1984,29,647-709.7 4.2.2 Asymptotic Spectral Distributions for Square Matrix Theorem 4.2.2. Let H be an N × N complex random matrix whose entries are independent random variables with identical mean, variance 1/N and finite kth moments for k ≥ 4. Then, the asymptotic spectrum of H converges almost surely to the circular law [2], namely the uniform distribution over the unit disk on the complex plane whose density is given by 1 ( ) C f    { : 1}     [2] V. L.Girko， Circular Law ［J］，Theory Prob. Appl.，1984，29，647 － 709．