From 90f728c17b2477aa9714fce514f93177bc802257 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 25 Jun 2024 17:11:10 +0200
Subject: More small changes.

---
 marginal.tex | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

(limited to 'marginal.tex')

diff --git a/marginal.tex b/marginal.tex
index 45d65dc..bc7c4ab 100644
--- a/marginal.tex
+++ b/marginal.tex
@@ -329,7 +329,7 @@ Extremizing this action over the new parameters $y$, $\Delta z$, and $\hat\lambd
     -\frac{\mu-\lambda^*}{2\sigma}\sqrt{\left(\frac{\mu-\lambda^*}{2\sigma}\right)^2-1}
   \right]
 \end{align}
-Inserting this solution into $\mathcal S_\infty$ we find
+Inserting this solution into the effective action we find
 \begin{equation} \label{eq:goe.large.dev}
   \begin{aligned}
     &G_{\lambda^*}(\mu)
@@ -342,8 +342,7 @@ Inserting this solution into $\mathcal S_\infty$ we find
   \end{aligned}
 \end{equation}
 This function is plotted in Fig.~\ref{fig:large.dev} for $\lambda^*=0$. For $\mu<2\sigma$ $G_{0}(\mu)$ has an
-imaginary part. This indicates that the existence of a marginal minimum for this
-parameter value corresponds with a large deviation that grows faster than $N$,
+imaginary part. This indicates that the existence of a minimally zero eigenvalue when $\mu<2\sigma$ corresponds with a large deviation that grows faster than $N$,
 rather like $N^2$, since in this regime the bulk of the typical spectrum is
 over zero and therefore extensively many eigenvalues have to have large
 deviations in order for the smallest eigenvalue to be zero. For
-- 
cgit v1.2.3-70-g09d2

