  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.
