From 101a3dd52c972252c3c606a51c33f87693d96c50 Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Wed, 9 Dec 2020 12:28:00 +0000
Subject: Update on Overleaf.

---
 bezout.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 6b817fd..753b65b 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -39,8 +39,7 @@ different topological properties.
 
 Spin-glasses have long been considered the paradigm of `complex landscapes' of many variables, a subject that
 includes Neural Networks and optimization problems, most notably  Constraint Satisfaction ones.
-The most tractable family of these  are the mean-field spherical p-spin models 
-
+The most tractable family of these  are the mean-field spherical p-spin models \cite{crisanti1992sphericalp} 
 defined by the energy:
 \begin{equation} \label{eq:bare.hamiltonian}
   H_0 = \sum_p \frac{c_p}{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
@@ -50,11 +49,12 @@ to a sphere $\sum_i z_i^2=N$. If there is a single  term of a given $p$, this is
 Also in the algebra \cite{cartwright2013number} and probability  literature \cite{auffinger2013complexity,auffinger2013random}
 
 This problem has been attacked from several angles: the replica trick to
-compute the Boltzmann--Gibbs distribution, a Kac--Rice \cite{Kac_1943_On,
+compute the Boltzmann--Gibbs distribution\cite{crisanti1992sphericalp}, a Kac--Rice \cite{Kac_1943_On,
 Rice_1939_The, Fyodorov_2004_Complexity} procedure (similar to the Fadeev--Popov
-integral)  to compute the number of saddle-points of the energy function, and
+integral)  to compute the number of saddle-points of the energy function
+\cite{crisanti1995thouless}, and
 the gradient-descent -- or more generally Langevin -- dynamics staring from a
-high-energy configuration.  Thanks to the relative simplicity of the energy,
+high-energy configuration \cite{cugliandolo1993analytical}.  Thanks to the relative simplicity of the energy,
 all these approaches are possible analytically in the large $N$ limit.
 
 In this paper we shall extend the study to the case  where $z\in\mathbb C^N$ are  and $J$ is a symmetric tensor
-- 
cgit v1.2.3-54-g00ecf

