From 5747a09486d70b3302d06757feb45aeca13475d0 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Mon, 7 Dec 2020 15:01:06 +0000 Subject: Update on Overleaf. --- bezout.tex | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index 3e68a10..7269454 100644 --- a/bezout.tex +++ b/bezout.tex @@ -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 dynami +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 -- cgit v1.2.3-54-g00ecf