summaryrefslogtreecommitdiff
diff options
context:
space:
mode:
-rw-r--r--bezout.tex3
1 files changed, 2 insertions, 1 deletions
diff --git a/bezout.tex b/bezout.tex
index 645ef15..783d547 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
+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