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.
Relaxational dynamics of the edwards-anderson model and the mean- field theory of spin-glasses.Physical Review B, 25(11):6860, 1982
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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.