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.bib | 31 +++++++++++++++++++++++++++++++
 bezout.tex | 10 +++++-----
 2 files changed, 36 insertions(+), 5 deletions(-)

diff --git a/bezout.bib b/bezout.bib
index 659e92b..37e8f33 100644
--- a/bezout.bib
+++ b/bezout.bib
@@ -174,3 +174,34 @@
   year={2004},
   publisher={APS}
 }
+@article{crisanti1995thouless,
+  title={Thouless-Anderson-Palmer approach to the spherical p-spin spin glass model},
+  author={Crisanti, Andrea and Sommers, H-J},
+  journal={Journal de Physique I},
+  volume={5},
+  number={7},
+  pages={805--813},
+  year={1995},
+  publisher={EDP Sciences}
+}
+@article{crisanti1992sphericalp,
+  title={The sphericalp-spin interaction spin glass model: the statics},
+  author={Crisanti, Andrea and Sommers, H-J},
+  journal={Zeitschrift f{\"u}r Physik B Condensed Matter},
+  volume={87},
+  number={3},
+  pages={341--354},
+  year={1992},
+  publisher={Springer}
+}
+
+@article{cugliandolo1993analytical,
+  title={Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model},
+  author={Cugliandolo, Leticia F and Kurchan, Jorge},
+  journal={Physical Review Letters},
+  volume={71},
+  number={1},
+  pages={173},
+  year={1993},
+  publisher={APS}
+}
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
-- 
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