The number of saddles of the spherical $p$-spin model
Probability
2020-07-21 v1
Abstract
We show that the quenched complexity of saddles of the spherical pure -spin model agrees with the annealed complexity when both are positive. Precisely, we show that the second moment of the number of critical values of a given finite index in a given interval has twice the growth rate of the first moment.
Keywords
Cite
@article{arxiv.2007.09269,
title = {The number of saddles of the spherical $p$-spin model},
author = {Antonio Auffinger and Julian Gold},
journal= {arXiv preprint arXiv:2007.09269},
year = {2020}
}
Comments
52 pages, 1 figure