36 research outputs found
On the Spectral Gap of Spherical Spin Glass Dynamics
We consider the time to equilibrium for the Langevin dynamics of the
spherical -spin glass model of system size . We show that the log-Sobolev
constant and spectral gap are order in at sufficiently high temperature
whereas the spectral gap decays exponentially in at sufficiently low
temperatures. These verify the existence of a dynamical high temperature phase
and a dynamical glass phase at the level of the spectral gap. Key to these
results are the understanding of the extremal process and restricted free
energy of Subag--Zeitouni and Subag.Comment: 21 page