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-rw-r--r--bezout.tex6
1 files changed, 3 insertions, 3 deletions
diff --git a/bezout.tex b/bezout.tex
index 1b9b078..213f9ef 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -249,7 +249,7 @@ elements of $J$ are standard complex normal, this corresponds to a complex
Wishart distribution. For $\kappa\neq0$ the problem changes, and to our
knowledge a closed form is not known. We have worked out an implicit form for
this spectrum using the saddle point of a replica symmetric calculation for the
-Green function. The result is
+Green function. {\color{red} the calculation is standard, we outline it in appendix xx} The result is
\begin{widetext}
\begin{equation}
G(\sigma)=\lim_{n\to0}\int d\alpha\,d\chi\,d\chi^*\frac\alpha2
@@ -259,7 +259,7 @@ Green function. The result is
\right\}
\end{equation}
\end{widetext}
-The argument of the exponential has several saddles, but the one with the smallest value of $\mathop{\mathrm{Re}}\alpha$ gives the correct solution \textcolor{red}{\textbf{why????? we never figured this out...}}.
+The argument of the exponential has several saddles, but the one with the smallest value of $\mathop{\mathrm{Re}}\alpha$ gives the correct solution \textcolor{red}{\textbf{we have checked this, but a detailed analysis of the saddle-point integration is still needed to justify it.}}.
The transition from a one-cut to two-cut singular value spectrum naturally
corresponds to the origin leaving the support of the eigenvalue spectrum.
@@ -328,7 +328,7 @@ Consider for example the ground-state energy for given $a$, that is, the energy
}
\end{figure}
-\begin{figure}[htpb]
+\begin{figure}[htpb]\label{
\centering
\includegraphics{fig/desert.pdf}
\caption{