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| -rw-r--r-- | frsb_kac-rice.tex | 6 |
1 files changed, 5 insertions, 1 deletions
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. |