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| -rw-r--r-- | bezout.tex | 3 |
1 files changed, 2 insertions, 1 deletions
@@ -47,7 +47,8 @@ where the $J_{i_1\cdots i_p}$ are real Gaussian variables and the $z_i$ are real to a sphere $\sum_i z_i^2=N$. This problem has been attacked from several angles: the replica trick to compute the Boltzmann-Gibbs distribution, -a Kac-Rice \cite{Kac,Fyodorov} procedure to compute the number of saddle-points of the energy function, and the +a Kac-Rice \cite{Kac,Fyodorov} procedure (similar to the Fadeev-Popov inte to compute the number of saddle-points of the energy function, and the gradient-descent -- or more generally Langevin -- dynamics staring from a high-energy configuration. +Thanks to the relative simplicity of the energy, all these approaches are possible analytically in the large $N$ limit. In th where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor |