From 5c85894386fdbb564b738b13af0e77a0bffe6c80 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 7 Jul 2022 20:33:21 +0200
Subject: Fixed small mistake in model introduction.

---
 frsb_kac-rice.tex | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 3b17093..c5a288b 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -60,8 +60,11 @@ Here we consider, for definiteness, the  mixed $p$-spin model, whose Hamiltonian
 \begin{equation}
   H(\mathbf s)=-\sum_p\frac1{p!}\sum_{i_1\cdots i_p}^NJ^{(p)}_{i_1\cdots i_p}s_{i_1}\cdots s_{i_p}
 \end{equation}
-is defined for vectors $\mathbf s\in\mathbb R^N$ confined to the sphere $\|\mathbf s\|^2=N$.
-The coupling coefficients are taken at random, with zero mean and covariance $\overline{(J^{(p)})^2}=a_pp!/2N^{p-1}$. This implies that the covariance of the energy with itself depends only on the dot product, or overlap, between two configurations, and in particular that
+is defined for vectors $\mathbf s\in\mathbb R^N$ confined to the sphere
+$\|\mathbf s\|^2=N$.  The coupling coefficients are taken at random, with zero
+mean and variance $\overline{(J^{(p)})^2}=a_pp!/2N^{p-1}$. This implies that
+the covariance of the energy with itself depends only on the dot product, or
+overlap, between two configurations, and in particular that
 \begin{equation}
   \overline{H(\mathbf s_1)H(\mathbf s_2)}=Nf\left(\frac{\mathbf s_1\cdot\mathbf s_2}N\right)
 \end{equation}
-- 
cgit v1.2.3-70-g09d2

