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-rw-r--r--bezout.tex11
1 files changed, 8 insertions, 3 deletions
diff --git a/bezout.tex b/bezout.tex
index 3d58342..36434e0 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -91,9 +91,14 @@ points it has is given by the usual Kac--Rice formula:
\partial_y\partial_x\mathop{\mathrm{Re}}H & \partial_y\partial_y\mathop{\mathrm{Re}}H
\end{bmatrix}\right|.
\end{equation}
-This expression is to be averaged over the $J$'s as
-$\Sigma=
-\overline{\ln \mathcal N_J} = \int dJ \; \ln N_J$, a calculation that involves the replica trick. In
+{\color{red} {\bf perhaps not here} This expression is to be averaged over the $J$'s as
+$N \Sigma=
+\overline{\ln \mathcal N_J} = \int dJ \; \ln N_J$, a calculation that involves the replica trick. In most, but not all, of the parameter-space that we shall study here, the {\em annealed approximation} $N \Sigma \sim
+\ln \overline{ \mathcal N_J} = \ln \int dJ \; N_J$ is exact.
+
+A useful propert
+
+}
The Cauchy--Riemann relations imply that the matrix is of the form:
\begin{equation} \label{eq:real.kac-rice1}