From 8066a95b169b00004efe8f15e0013618eff37a02 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 7 Dec 2020 16:00:58 +0100
Subject: Changed the form of the elliptical constraint.

---
 bezout.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'bezout.tex')

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}.
 
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cgit v1.2.3-54-g00ecf

