All Questions
7 questions
6
votes
1
answer
1k
views
Largest eigenvalues of a (random) correlation matrix?
I am recently studying on eigenvalues of a (random) correltion matrix. For a $N\times N$ correlation matrix (with a given meaning of randomness), its (1st, 2nd, etc.) eigenvalues have some ...
- 380
4
votes
1
answer
294
views
Finding high-dimensional correlation matrices that are both sparse and low-rank
Let $\boldsymbol{R}$ be the correlation matrix of $X_i,i=1,\dots,p$ with a large $p\gg q=\text{rank}(\boldsymbol{R})$. Is that reasonable to assume that $\boldsymbol{R}$ is both (approximately) sparse ...
- 193
3
votes
2
answers
580
views
Largest eigenvalue of the adjacency matrix of weighted random graph
I find the theorem for largest eigenvalue of the adjacency matrix of ER random graph in here https://arxiv.org/pdf/math/0106066.pdf. The adjacency matrix is a symmetric random matrix s.t. diagonal ...
- 272
3
votes
0
answers
151
views
Largest eigenvalue divided by $n$
Let $X$ be an $n\times n$ symmetric random matrix whose diagonal is fixed as $1$, and every element in the upper triangle (excluding the diagonal) is drawn from Bernoulli($p$). The elements in the ...
- 272
3
votes
0
answers
435
views
Rank of Hadamard product with random matrices
I do research in statistics and am not sure whether the following is considered research level or not in mathematics. If it isn't, I'm happy because that means the answer is probably known and I can ...
- 131
2
votes
1
answer
583
views
What are the origin and applications of this result?
In a course taught by Morris Eaton on multivariate statistics that dealt mostly with the Wishart distribution, I learned this proposition: Suppose
$$ M = \begin{bmatrix} A & B \\\\ B^T & C \...
1
vote
0
answers
80
views
Moments from characteristic function for matrices
When $x$ is a random variable with the smooth characteristic function $\phi_x(t) = \mathbb{E}e^{itx}$, we can easily compute the moments as $\mathbb{E}[x^k] = i^{-n}\phi_x^{(n)}(0)$. There is no magic ...
- 193