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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-07 16:00:58 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-07 16:00:58 +0100
commit8066a95b169b00004efe8f15e0013618eff37a02 (patch)
tree7ed86208fca397709b8a73c5ace9bc8740068e66
parented825197b5e91df4dfb774e577496a5813bf2e2b (diff)
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Changed the form of the elliptical constraint.
-rw-r--r--bezout.tex6
1 files changed, 3 insertions, 3 deletions
diff --git a/bezout.tex b/bezout.tex
index d3bb47d..645ef15 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -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}.