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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-07 15:53:30 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-07 15:53:30 +0100
commitcd83d96a1e8b425601c059241882b87e0d572860 (patch)
treeb0ff74a5030317a94a436c84af4dd1af9f016985
parent7b41b5b8463a5ed3f393f50aba3e8337a5d6fd15 (diff)
parent0d7940769f72b56ad01f2ac8d950b238074a322e (diff)
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Merge branch 'master' of https://git.overleaf.com/5fcce4736e7f601ffb7e1484
-rw-r--r--bezout.tex5
1 files changed, 3 insertions, 2 deletions
diff --git a/bezout.tex b/bezout.tex
index fd7f56c..7e932ea 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -39,10 +39,11 @@ different topological properties.
Spin-glasses have long been considered the paradigm of `complex landscapes' of many variables, a subject that
includes Neural Networks and optimization problems, most notably Constraint Satisfaction ones.
-The most tractable, yet very rich model
+The most tractable family of these are the mean-field spherical p-spin models defined by the energy:
\begin{equation} \label{eq:bare.hamiltonian}
- H_0 = \frac1{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
+ E = \sum_p \frac{c_p}{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p},
\end{equation}
+where the $J_{i_1\cdots i_p}$ are
where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor
whose elements are complex normal with $\langle|J|^2\rangle=p!/2N^{p-1}$ and
$\langle J^2\rangle=\kappa\langle|J|^2\rangle$ for complex parameter