A revisit of the circular law
A revisit of the circular law
Consider a complex random $n\times n$ matrix ${\bf X}_n=(x_{ij})_{n\times n}$, whose entries $x_{ij}$ are independent random variables with zero means and unit variances. It is well-known that Tao and Vu (Ann Probab 38: 2023-2065, 2010) resolved the circular law conjecture, establishing that if the $x_{ij}$'s are independent and identically distributed …