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4 questions
3
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General formula for the integral w.r.t to Marchenko-Pastur density, of the ratio of degree $\le 2$ polynomials
Question. Is there a closed-form formula (via standard objects like rational functions, radicals, special functions, special numbers like Catalan numbers, etc.) expressing integrals of rational ...
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2
votes
1
answer
213
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For fixed $\lambda \ge 0$, Integrate the function $f_\lambda(x):=x/(x + \lambda)^2$ w.r.t. Marchenko-Pastur density
In trying to solve another the problem posed in the question https://www.mathoverflow.net/q/385777/78539, I'm led to consider the following problem.
Let $\mu_\gamma$ be the Marchenko-Pastur ...
- 6,853
3
votes
1
answer
354
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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 ...
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17
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1
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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 ...
