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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-07 16:01:13 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-07 16:01:13 +0100 |
commit | 471e49b1a172752c58439733e9f81f9255b539f3 (patch) | |
tree | 427d42c6e6d1fd7046c26b5eb44f9c7773069295 | |
parent | 8066a95b169b00004efe8f15e0013618eff37a02 (diff) | |
parent | 5747a09486d70b3302d06757feb45aeca13475d0 (diff) | |
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Merge branch 'master' of https://git.overleaf.com/5fcce4736e7f601ffb7e1484
-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 |