From 8d06423bf6291ccd11696b9012bc054c5eee963f Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" <kurchan.jorge@gmail.com>
Date: Mon, 24 Oct 2022 10:27:52 +0000
Subject: Update on Overleaf.

---
 frsb_kac-rice_letter.tex | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

(limited to 'frsb_kac-rice_letter.tex')

diff --git a/frsb_kac-rice_letter.tex b/frsb_kac-rice_letter.tex
index 84d708d..63b7811 100644
--- a/frsb_kac-rice_letter.tex
+++ b/frsb_kac-rice_letter.tex
@@ -27,7 +27,7 @@
 
 \begin{abstract}
   Complexity is a measure of the number of stationary points in complex
-  landscapes. We derive a general solution for the complexity of mean-field
+  landscapes. We {\color{red} solve the long-standing problem of detremining the...} derive a general solution for the complexity of mean-field
   complex landscapes. It incorporates Parisi's solution for the ground state,
   as it should. Using this solution, we count the stationary points of two
   models: one with multi-step replica symmetry breaking, and one with full
@@ -95,8 +95,8 @@ models have $a_p=1$ for some $p$ and all others zero.
 
 The complexity of the $p$-spin models has been extensively studied by
 physicists and mathematicians. Among physicists, the bulk of work has been on
-the so-called Thouless--Anderson--Palmer (TAP) complexity for the pure models,
-which counts minima in a kind of mean-field free energy \cite{Rieger_1992_The,
+ the so-called  `TAP' complexity, 
+which counts minima in the mean-field Thouless--Anderson--Palmer () free energy \cite{Rieger_1992_The,
 Crisanti_1995_Thouless-Anderson-Palmer, Cavagna_1997_An,
 Cavagna_1997_Structure, Cavagna_1998_Stationary, Cavagna_2005_Cavity,
 Giardina_2005_Supersymmetry}. The landscape complexity has been proven for pure
@@ -165,7 +165,7 @@ population of stationary points suddenly shifts from all saddles to all minima,
 and there is an abrupt percolation transition in the topology of
 constant-energy slices of the landscape. This behavior of the complexity can be
 used to explain a rich variety of phenomena in the equilibrium and dynamics of
-the pure models: the threshold energy $E_\mathrm{th}$ corresponds to the
+the pure models: the `threshold' \cite{Cugliandolo_1993_Analytical} energy $E_\mathrm{th}$ corresponds to the
 average energy at the dynamic transition temperature, and the asymptotic energy
 reached by slow aging dynamics.
 
-- 
cgit v1.2.3-70-g09d2

