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.
Fundamental limits of detection in the spiked Wigner model.The Annals of Statistics, 48(2):863 – 885, 2020
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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.