From 835a7763c2bc061251bf8a678037ef0ab3a614ba Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 13 Jul 2022 13:33:04 +0200
Subject: Slightly nicer typesetting of bad equations.

---
 frsb_kac-rice.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 7e260f9..752a7ae 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -860,9 +860,9 @@ as we expand the extremal conditions, using \eqref{eq:replica.det.cont} to
 treat the determinant. To quadratic order, this gives
 \begin{equation}
   \begin{aligned}
-  \Sigma(E,\mu^*)
+  &\Sigma(E,\mu^*)
   =\mathcal D(\mu^*)+\hat\beta E-\mu r_d+\frac12\left[\hat\beta^2f(1)+(2\hat\beta r_d-d_d)f'(1)+r_d^2f''(1)\right]+\frac12\ln(d_d+r_d^2) \\
-  -\frac12\left[
+  &-\frac12\left[
     \frac12\hat\beta^2\bar c^2f''(0)+(2\hat\beta\bar r-\bar d)\bar cf''(0)+\bar r^2f''(0)
     -\frac{\bar d^2-2d_d\bar r^2+d_d^2\bar c^2+4r_d\bar r(\bar d+d_d\bar c)-2r_d^2(\bar c\bar d+\bar r^2)}{2(d_d+r_d^2)^2}
   \right]x_\textrm{max}^2
-- 
cgit v1.2.3-70-g09d2

