# Tagged Questions

Statistics of spectral properties of matrix-valued random variables.

2k views

### When should we expect Tracy-Widom?

The Tracy-Widom law describes, among other things, the fluctuations of maximal eigenvalues of many random large matrix models. Because of its universal character, it obtained his position on the ...
2k views

832 views

### Probability of random (0,1) Toeplitz matrix being invertible

A Toeplitz matrix or diagonal-constant matrix is a matrix in which each descending diagonal from left to right is constant. What is the probability that a random $n \times n$ binary Toeplitz ...
179 views

### Expected size of determinant of $AA^T$ for non-square random $A$
If $A$ is chosen uniformly at random over all possible $m$ by $n$ (0,1)-matrices, what is the expected size of the absolute value of the determinant of $AA^T$. We can assume $m < n$ and all ...
Suppose we have a a set of random matrices in the complex field of the form $a_iv_iv_i^H$ for $i=\{1,\dots,n\}$ where $a_i$ are constant positive real scalars and $v_i$ are random complex valued ...