Some tweaks and new title proposal

1 files changed, 17 insertions, 9 deletions

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 23a41d4..6880717 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -15,7 +15,10 @@
 \addbibresource{frsb_kac-rice.bib}
 
 \begin{document}
-\title{Full solution for counting stationary points of mean-field complex energy landscapes}
+\title{Full solution for counting stationary points of mean-field complex energy landscapes\\
+  \textit{or (fun title)} \\
+  How to count in hierarchical landscapes: a `full' solution to mean-field complexity
+}
 \author{Jaron Kent-Dobias \& Jorge Kurchan}
 \maketitle
 \begin{abstract}
@@ -25,14 +28,19 @@
 \section{Introduction}
 
 The computation of the number of metastable states of mean field spin glasses
-goes back to the beginning of the field. Over forty years ago,
-Bray and Moore \cite{Bray_1980_Metastable} attempted the first calculation for 
- the Sherrington--Kirkpatrick model, in a paper remarkable for being one of the first applications of a replica symmetry breaking scheme. As became clear when the actual ground-state of the model was computed by Parisi \cite{Parisi_1979_Infinite} with a different scheme, the Bray--Moore result
- was not exact, and in fact  the problem has been open ever since.
-To this date the program of computing the number of saddles of a mean-field 
-glass has been only  carried out for a small subset of models, including most notably the (pure) $p$-spin model ($p>2$) \cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer}. 
-In a parallel development, it 
-has evolved into an active field in probability theory \cite{Auffinger_2012_Random, Auffinger_2013_Complexity, BenArous_2019_Geometry}
+goes back to the beginning of the field. Over forty years ago, Bray and Moore
+\cite{Bray_1980_Metastable} attempted the first calculation for the
+Sherrington--Kirkpatrick model, in a paper remarkable for being one of the
+first applications of a replica symmetry breaking scheme. As became clear when
+the actual ground-state of the model was computed by Parisi
+\cite{Parisi_1979_Infinite} with a different scheme, the Bray--Moore result was
+not exact, and in fact  the problem has been open ever since.  To this date the
+program of computing the number of saddles of a mean-field glass has been only
+carried out for a small subset of models, including most notably the (pure)
+$p$-spin model ($p>2$) \cite{Rieger_1992_The,
+Crisanti_1995_Thouless-Anderson-Palmer}.  In a parallel development, it has
+evolved into an active field in probability theory \cite{Auffinger_2012_Random,
+Auffinger_2013_Complexity, BenArous_2019_Geometry}.
 
 In this paper we present what we argue is the general replica ansatz for the 
 computation of the number of saddles of generic mean-field models,  which we expect to include the Sherrington--Kirkpatrick model. It reproduces  the Parisi result in the limit