From 4ad9a04821a4f1d3e8a52d41e0eafc1b38eba7ea Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Sun, 13 Dec 2020 10:43:55 +0000
Subject: Update on Overleaf.

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

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 2c10de4..4ec1f46 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -118,7 +118,7 @@ We see from (\ref{cosa}) that at any critical point, $\epsilon=H/N$, the average
 Since $H$ is holomorphic, any critical point of $\operatorname{Re}H$ is also a
 critical point of $\operatorname{Im}H$. The number of critical points of $H$ is
 therefore the same as that of $\operatorname{Re}H$. From each saddle 
-emerges a gradient line of $\operatorname{Re}H$, which is also one of constant
+emerge a gradient lines of $\operatorname{Re}H$, which is also one of constant
 $\operatorname{Im}H$ and therefore constant phase.
 
 Writing $z=x+iy$, $\operatorname{Re}H$ can be considered a real-valued function
@@ -441,7 +441,7 @@ threshold level, where the system develops a mid-spectrum gap, will play a
 crucial role as it does in the real case.
 
 \begin{acknowledgments}
-We wish to thank Alexander Altland for a useful suggestion.
+We wish to thank Alexander Altland, Satya Majumdar and Gregory Schehr for a useful suggestions.
   JK-D and JK are supported by the Simons Foundation Grant No.~454943.
 \end{acknowledgments}
 
-- 
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