From b5ed2657de0830d2305dba9db362aa3d75883cc3 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Thu, 7 Jul 2022 14:08:56 +0000 Subject: Update on Overleaf. --- frsb_kac-rice.tex | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) (limited to 'frsb_kac-rice.tex') diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 9e9d40d..ec2b26f 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -887,7 +887,11 @@ the probability distribution of the overlaps between stationary points $P(q)$. F \begin{equation} P(q)=\frac1{\mathcal N^2}\sum_{\sigma,\sigma'}\delta\left(\frac{s_\sigma\cdot s_{\sigma'}}N-q\right) \end{equation} -where the sum is twice over stationary points $\sigma$ and $\sigma'$. It is +where the sum is twice over stationary points $\sigma$ and $\sigma'$. +{\em This is the probability that two stationary points randomly drawn from the ensemble +of stationary points happen to be at overlap $q$} + +It is straightforward to show that moments of this distribution are related to certain averages of the form. These are evaluated for a given energy, index, etc, but we shall omit these subindices for simplicity. -- cgit v1.2.3-70-g09d2