Circular law

In probability theory, more specifically the study of random matrices, the circular law concerns the distribution of eigenvalues of an ${\displaystyle n\times n}$ random matrix with independent and identically distributed entries in the limit ${\displaystyle n\to \infty }$.

It asserts that for any sequence of random n × n matrices whose entries are independent and identically distributed random variables, all with mean zero and variance equal to 1/n, the limiting spectral distribution is the uniform distribution over the unit disc.