# Tagged Questions

**0**

votes

**1**answer

126 views

### How to calculate eigenvalue density function of $XX^\dagger$ from the density function of X

Let X be a complex random matrix, which has the probability function (drawn from the ensemble) V($XX^\dagger$), where V(x) is some function which guaranties good behavior at infinity. Note the unitary ...

**4**

votes

**2**answers

821 views

### Eigenvalues of random Hamiltonian matrices

A real $2n\times 2n$ Hamiltonian matrix has the general form
$$H=\begin{pmatrix}
A & B \cr
C & -A^T
\end{pmatrix}
$$
where $A$, $B$ and $C$ are $n\times n$ matrices, and $B$ and $C$ are ...

**2**

votes

**2**answers

676 views

### Singular Value Decomposition of Noisy Matrices

I am an engineer who makes measurements of a variable over a grid
of, say, $m\times n$. Since these are actual measurements, the true
values are always corrupted by noise, and what I measure is a ...

**1**

vote

**0**answers

58 views

### Random Schrödinger operators with asymmetric Lifshitz tails?

For a quantum mechanical system with a periodic Hamiltonian (SchrÃ¶dinger operator) $H$, let $N(E)$ be its integrated density of states, i.e. the fraction of eigenvalues in the spectrum $\sigma(H)$ ...

**21**

votes

**0**answers

903 views

### Correspondence between eigenvalue distributions of random unitary and random orthogonal matrices

In the course of a physics problem (arXiv:1206.6687), I stumbled on a curious correspondence between the eigenvalue distributions of the matrix product $U\bar{U}$, with $U$ a random unitary matrix and ...

**0**

votes

**1**answer

393 views

### Spectral theory of real symmetric matrices with random diagonal elements

Can you point me in the direction of any research done on the spectral theory (i.e. eigenvalues and eigenvectors) of real symmetric matrices with random (Gaussian or Levy) diagonal elements and fixed ...

**6**

votes

**1**answer

570 views

### Does random matrix theory make any prediction for the eigenvalue distributions of compact Riemann surfaces?

Under RH, Montgomery has proven equidistribution results for the zeros of the Riemann Zeta function, which suggest a close connection of the distribution to certain results in Random matrix theory. ...

**4**

votes

**2**answers

568 views

### Distribution of eigenvalue spacings

I have been doing some experiments on classes of random matrices, and it seems (visually) that the distribution of eigenvalue spacings is consistent with GOE or GUE or GSE. Unfortunately, to test ...

**7**

votes

**0**answers

520 views

### Matrix integral identity

1) How to prove that $N\times N$ matrix integral over complex matrices $Z$
$$
\int d Z d Z^\dagger e^{-Tr Z Z^\dagger} \frac{x_1\det e^Z -x_2 \det ...

**5**

votes

**2**answers

493 views

### Dependence of trace norm on matrix size for smooth vs. random matrices.

Problem
Consider two d x d complex matrices, R and S, whose entries lie in the unit disk:
$\quad |R_{i,j}|<1 \quad$ and $\quad |S_{i,j}|<1 $.
Say that R is constructed by randomly choosing ...