From ebfd67bfdd46235c8a502855d645a2a851a31d7d Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Mon, 7 Dec 2020 14:57:43 +0000 Subject: Update on Overleaf. --- bezout.tex | 3 +++ 1 file changed, 3 insertions(+) diff --git a/bezout.tex b/bezout.tex index e4aead7..8acee10 100644 --- a/bezout.tex +++ b/bezout.tex @@ -46,6 +46,9 @@ The most tractable family of these are the mean-field spherical p-spin models d where the $J_{i_1\cdots i_p}$ are real Gaussian variables and the $z_i$ are real and constrained 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 + In th where $z\in\mathbb C^N$ is constrained by $z^2=N$ and $J$ is a symmetric tensor whose elements are complex normal with $\langle|J|^2\rangle=p!/2N^{p-1}$ and -- cgit v1.2.3-70-g09d2