From 698f74a6f5abf481d860540850b202f6e66e01f3 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 7 Jun 2022 08:14:30 +0200
Subject: Tiny fix.

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

(limited to 'frsb_kac_new.tex')

diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex
index 99455de..f5e9422 100644
--- a/frsb_kac_new.tex
+++ b/frsb_kac_new.tex
@@ -400,9 +400,9 @@ Consider the extremum problem of \eqref{eq:diagonal.action} with respect to $R_d
   =-\frac12f'(1)+\frac12\frac1{R_d^2}\lim_{n\to0}\frac1n\operatorname{Tr}((D_d/R_d^2)Q+I)^{-1}Q \label{eq:saddle.d}\\
   0
   &=\frac{\partial S}{\partial R_d}
-  =-\mu+\hat\epsilon f'(1)+R_df''(1)+\frac1{R_d}+\frac{D_d}{R_d}\lim_{n\to0}\frac1n\operatorname{Tr}((D_d/R_d^2)Q+I)^{-1}Q \label{eq:saddle.r}
+  =-\mu+\hat\epsilon f'(1)+R_df''(1)+\frac1{R_d}-\frac{D_d}{R_d^3}\lim_{n\to0}\frac1n\operatorname{Tr}((D_d/R_d^2)Q+I)^{-1}Q \label{eq:saddle.r}
 \end{align}
-Adding $2(D_d/R_d)$ of \eqref{eq:saddle.d} to \eqref{eq:saddle.r} and multiplying by $R_d$ gives
+Adding $2(D_d/R_d)$ times \eqref{eq:saddle.d} to \eqref{eq:saddle.r} and multiplying by $R_d$ gives
 \begin{equation}
   0=-R_d\mu+1+R_d^2f''(1)+f'(1)(R_d\hat\epsilon-D_d)
 \end{equation}
-- 
cgit v1.2.3-70-g09d2

