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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-07 16:00:58 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-07 16:00:58 +0100 |
commit | 8066a95b169b00004efe8f15e0013618eff37a02 (patch) | |
tree | 7ed86208fca397709b8a73c5ace9bc8740068e66 | |
parent | ed825197b5e91df4dfb774e577496a5813bf2e2b (diff) | |
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Changed the form of the elliptical constraint.
-rw-r--r-- | bezout.tex | 6 |
1 files changed, 3 insertions, 3 deletions
@@ -111,9 +111,9 @@ which makes its ensemble that of Gaussian complex symmetric matrices. Given its $\langle|\partial_i\partial_j H_0|^2\rangle=p(p-1)a^{p-2}/2N$ and $\langle(\partial_i\partial_j H_0)^2\rangle=p(p-1)\kappa/2N$, $\rho_0(\lambda)$ is constant inside the ellipse \begin{equation} \label{eq:ellipse} - \left(\frac{\mathop{\mathrm{Re}}(\lambda e^{i\theta})}{1+|\kappa|/a^{p-2}}\right)^2+ - \left(\frac{\mathop{\mathrm{Im}}(\lambda e^{i\theta})}{1-|\kappa|/a^{p-2}}\right)^2 - <\frac12p(p-1)a^{p-2} + \left(\frac{\mathop{\mathrm{Re}}(\lambda e^{i\theta})}{a^{p-2}+|\kappa|}\right)^2+ + \left(\frac{\mathop{\mathrm{Im}}(\lambda e^{i\theta})}{a^{p-2}-|\kappa|}\right)^2 + <\frac{p(p-1)}{2a^{p-2}} \end{equation} where $\theta=\frac12\arg\kappa$ \cite{Nguyen_2014_The}. |