Langevin dynamics on spiked Wigner matrices achieve O(log N) mixing from symmetric initializations even below the critical temperature, while worst-case mixing times are exponential with rate equal to the free-energy difference between spiked and null models.
Symmetric langevin spin glass dynamics.The Annals of Probability, 25(3):1367– 1422, 1997
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Mixing times of Langevin dynamics for spiked matrix models
Langevin dynamics on spiked Wigner matrices achieve O(log N) mixing from symmetric initializations even below the critical temperature, while worst-case mixing times are exponential with rate equal to the free-energy difference between spiked and null models.