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Results tagged with integration
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user 142153
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
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Spectrum of large random asymmetric matrices with correlation
Background:
In their paper, Sommers Crisanti Sompolinsky and Stein derive the spectral distribution of large random matrices $\mathbf{J}$ by studying the following integral:
\begin{equation}
I=\left[ …
- 117
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Solving integral equation with an unknown probability distribution
Considering this system of integral equations, where $\gamma \in \mathbb{R} $ and $\alpha\in \mathbb{C}$ are the unknown to solve :
$$ 1=\int_{-\infty}^{\infty} p(u) \frac{ -1}{\gamma-\left(u-z^{*}+\t …
- 117
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Solving the inverse of a matrix under a uniform distribution
My main issue is that after integration there are $\arctan$'s coming along the way and I do not know how/if analytical solutions can be found. …
- 117
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How can we do a Gaussian integral over matrix elements?
I am integrating the following Gaussian over all possible matrix elements $J_{ij}$:
$$ I=\int \exp{\left\{-a\sum_{ij}J_{ij}^2+b\sum_{ij}J_{ij}+c\sum_{ij}J_{ij}J_{ji} \right\}} \left (\prod_{ij}\mathrm …
- 117