Added sentence clarifying that H is centered.

1 files changed, 2 insertions, 1 deletions

diff --git a/when_annealed.tex b/when_annealed.tex
index 762c99e..0b1e52a 100644
--- a/when_annealed.tex
+++ b/when_annealed.tex
@@ -102,6 +102,7 @@ product (or overlap) between the two configurations:
 \begin{equation} \label{eq:covariance}
   \overline{H(\pmb\sigma_1)H(\pmb\sigma_2)}=\frac1Nf\bigg(\frac{\pmb\sigma_1\cdot\pmb\sigma_2}N\bigg)
 \end{equation}
+We will further take the distribution of $H$ to be centered, i.e., $\overline{H(\pmb\sigma)}=0$ for all $\pmb\sigma\in S^{N-1}$, which is equivalent to the absence of any deterministic term (or spike) in the function.
 Specifying the covariance function $f$ uniquely specifies the model. The series
 coefficients of $f$ need to be nonnnegative in order for $f$ to be a
 well-defined covariance. The case where $f$ is a homogeneous polynomial has
@@ -122,7 +123,7 @@ called $3+s$ models.\footnote{
   trivial overlap $q_0$ is also important in situations where a deterministic
   field (or spike) is present, as in \cite{Ros_2019_Complex}, but deterministic
   fields are likewise not considered here.
-}These are examples of \emph{mixed} spherical models, which have been studied
+} These are examples of \emph{mixed} spherical models, which have been studied
 in the physics and statistics literature and host a zoo of complex orders and
 phase transitions \cite{Crisanti_2004_Spherical, Crisanti_2006_Spherical,
   Krakoviack_2007_Comment, Crisanti_2007_Amorphous-amorphous,