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| -rw-r--r-- | bezout.tex | 2 |
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@@ -23,7 +23,7 @@ \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}. |