From 2a57d9283f23e211ce8e00e32869ba54b0296a08 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 7 Jun 2022 18:23:19 +0200
Subject: Readded expression for D(mu).
---
frsb_kac_new.tex | 6 +++++-
1 file changed, 5 insertions(+), 1 deletion(-)
(limited to 'frsb_kac_new.tex')
diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex
index 552ee9b..e1c5768 100644
--- a/frsb_kac_new.tex
+++ b/frsb_kac_new.tex
@@ -295,7 +295,11 @@ Introducing the parameters:
\begin{aligned}
\mathcal D(\mu)
&=\frac1N\overline{\log|\det(\partial\partial H(s_a)+\mu I)|}
- =\int d\lambda\,\rho(\lambda+\mu)\log|\lambda|
+ =\int d\lambda\,\rho(\lambda+\mu)\log|\lambda| \\
+ &=\operatorname{Re}\left\{
+ \frac12\left(1+\frac\mu{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right)
+ -\log\left(\frac1{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right)
+ \right\}
\end{aligned}
\end{equation}
--
cgit v1.2.3-70-g09d2