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authorkurchan.jorge <kurchan.jorge@gmail.com>2020-12-09 14:31:48 +0000
committeroverleaf <overleaf@localhost>2020-12-09 14:32:38 +0000
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Update on Overleaf.
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\date\today
\begin{abstract}
- We study the saddle-points of the $p$-spin mode -- the best understood example of `complex (rugged) landscape' -- in the space in which all its $N$ variables are allowed to be complex. The problem becomes
+ We study the saddle-points of the $p$-spin model -- the best understood example of `complex (rugged) landscape' -- in the space in which all its $N$ variables are allowed to be complex. The problem becomes
a system of $N$ random equations of degree $p-1$.
We solve for quantities averaged over randomness in the $N \rightarrow \infty$ limit.
We show that the number of solutions saturates the Bézout bound $\ln {\cal{N}}\sim N \ln (p-1) $\cite{Bezout_1779_Theorie}.