From d733e935e1c9032761ad5b09377ed7b3111f97d0 Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Mon, 7 Dec 2020 14:57:56 +0000
Subject: Update on Overleaf.

---
 bezout.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 8acee10..3e68a10 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -47,7 +47,7 @@ where the $J_{i_1\cdots i_p}$ are real Gaussian variables and the $z_i$ are real
 to a sphere $\sum_i z_i^2=N$.
 
 This problem has been attacked from several angles: the replica trick to compute the Boltzmann-Gibbs distribution,
-a Kac-Rice \cite{Kac,Fyodorov} procedure to compute the number of saddle-points of the energy function, and the  
+a Kac-Rice \cite{Kac,Fyodorov} procedure to compute the number of saddle-points of the energy function, and the dynami 
 
 In th
 where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor
-- 
cgit v1.2.3-54-g00ecf


From 5747a09486d70b3302d06757feb45aeca13475d0 Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Mon, 7 Dec 2020 15:01:06 +0000
Subject: Update on Overleaf.

---
 bezout.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 3e68a10..7269454 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -47,7 +47,8 @@ where the $J_{i_1\cdots i_p}$ are real Gaussian variables and the $z_i$ are real
 to a sphere $\sum_i z_i^2=N$.
 
 This problem has been attacked from several angles: the replica trick to compute the Boltzmann-Gibbs distribution,
-a Kac-Rice \cite{Kac,Fyodorov} procedure to compute the number of saddle-points of the energy function, and the dynami 
+a Kac-Rice \cite{Kac,Fyodorov} procedure (similar to the Fadeev-Popov inte to compute the number of saddle-points of the energy function, and the gradient-descent -- or more generally Langevin -- dynamics staring from a high-energy configuration.
+Thanks to the relative simplicity of the energy, all these approaches are possible analytically in the large $N$ limit.
 
 In th
 where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor
-- 
cgit v1.2.3-54-g00ecf

