5
votes
1answer
392 views

Characteristic polynomials of certain random symmetric matrices and the complexity of random Morse functions

Investigations concerning random Morse functions led me to the following problem. Consider the classical GOE of $m\times m$ real symmetric matrices $A$ with independent Gaussian entries with ...
4
votes
2answers
273 views

analogue of GUE and Ginibre in higher dimensions

This is a completely unmotivated question, but what happens to the 1-point marginal distribution for the following $N$-point joint distribution: $$\displaystyle p(z_1,\ldots, z_N) = C_N ...
2
votes
1answer
238 views

Why doesn't the argument of circular law convergence of Ginibre spectrum give the same result for GUE?

It appears I am profoundly confused in the following nice argument of Ginibre and Mehta and beautifully presented in Djalil Chafai's blog ...
5
votes
1answer
253 views

Expected inverse determinant with independent rows

Let $a_1,a_2,\dots,a_n$ be independent identically distributed random vectors in $\mathbb R^n$. I need a bound for $E[|\det A|^{-1}]$, where $A$ is the matrix composed out of these vectors. More ...