2
votes
1answer
181 views

Determining the asymptotic behavior of random matrices with vanishing ratio dimensions

Consider an $N\times K$ random matrix $X$ (defined on a probability space $(Ω,F,μ)$) with i.i.d. entries having zero mean and variance $1/K$. There are a lot of results regarding the asymptotic ...
3
votes
0answers
128 views

On the multidimensional Mellin transform of measures

Consider an integral transform of Borel measures supported on $\mathbb{R}^n_+$ given by $$ f(z) =\int\limits_{\mathbb{R}^n_+} x^{z}\frac{\mu(dx)}{x} $$ where $z = (z_1,...,z_n) \in \mathbb{C}^n$, ...
1
vote
0answers
214 views

On the generalisation of the Laplace transform

I consider a measure transform $A$ given by $$ A\mu(x) = \int\limits_{\mathbb{R}^n_{+}} e^{-g(x,y)} \mu(dy) $$ where $g(x,y)$ is some positive smooth function, $\mu$ is a Borel measure. Is it a ...
3
votes
1answer
1k views

Intuitive understanding of the Stieltjes transform

I have been using random matrix theory in signal processing and have some trouble understanding what the Stieltjes transform does. The gist of my work is that I have an $N\times N$ true covariance ...