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Circular law : ウィキペディア英語版
Circular law
In probability theory, more specifically the study of random matrices, the circular law describes the distribution of eigenvalues of an random matrix with independent and identically distributed entries in the limit
.
It asserts that for any sequence of whose entries are independent and identically distributed random variables, all with mean zero and variance equal to , the limiting spectral distribution is the uniform distribution over the unit disc.
==Precise statement==
Let (X_n)_^\infty be a sequence of matrix ensembles whose entries are i.i.d. copies of a complex random variable with mean 0 and variance 1. Let \lambda_1, \ldots, \lambda_n, 1 \leq j \leq n denote the eigenvalues of \displaystyle \frac(A) = n^ \#\~, \quad A \in \mathcal(\mathbb).
With these definitions in mind, the circular law asserts the sequence of measures \displaystyle \mu_} X_n}(x,y) converges in probability to the uniform measure on the unit disk.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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