Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Consider $A$ a $n \times n$ random matrix with centered Gaussian entries $A_{i,j}$ such that $$\mathbb{E}[A_{i,j}^2]=\sigma_j^2/n$$

The variances depend on the column only.

What do we know on the eigenvalues distribution ? In particular, if one assumes that $$\frac{1}{n}\sum_{j=1}^n \sigma_j^2 \to \bar{\sigma}^2$$ then is it true that :

$\rho(A):=max(|\lambda_k|) \to \bar{\sigma}^2$ when $n\to \infty$ ?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.