Analyzing dynamics and average case complexity in the spherical Sherrington-Kirkpatrick model: a focus on extreme eigenvectors
Probability
2024-01-09 v1 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
We explore Langevin dynamics in the spherical Sherrington-Kirkpatrick model, delving into the asymptotic energy limit. Our approach involves integro-differential equations, incorporating the Crisanti-Horner-Sommers-Cugliandolo-Kurchan equation from spin glass literature, to analyze the system's size and its temperature-dependent phase transition. Additionally, we conduct an average case complexity analysis, establishing hitting time bounds for the bottom eigenvector of a Wigner matrix. Our investigation also includes the power iteration algorithm, examining its average case complexity in identifying the top eigenvector overlap, with comprehensive complexity bounds.
Keywords
Cite
@article{arxiv.2401.03668,
title = {Analyzing dynamics and average case complexity in the spherical Sherrington-Kirkpatrick model: a focus on extreme eigenvectors},
author = {Tingzhou Yu},
journal= {arXiv preprint arXiv:2401.03668},
year = {2024}
}