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For large, order-$1$, signal-to-noise, the (worst-case) mixing time undergoes a sharp transition around the critical inverse temperature $\\beta_c(\\theta) = \\frac{1}{\\theta}$. Namely, if $\\beta = \\alpha/\\theta$, and $\\alpha<1$ then at large $\\theta$ the mixing time is $O(\\log N)$, and if $\\alpha>1$ it is exponential in $N$. We show that initialized from the uniform-at-random spherical prior, however, the mixing time in the low-temperatu","authors_text":"Curtis Grant, Reza Gheissari, Tianmin Yu","cross_cats":[],"headline":"Langevin dynamics for large-signal spiked matrices mix in O(log N) from uniform spherical starts even below the critical temperature.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-21T21:36:21Z","title":"Mixing times of Langevin dynamics for spiked matrix models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.20008","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T01:01:16.493406Z","id":"704584ca-020c-4ed8-a2f1-df676bd17f3c","model_set":{"reader":"grok-4.3"},"one_line_summary":"For spiked Wigner matrices, Langevin dynamics mixes in O(log N) time from uniform or top-eigenvector-symmetric starts below the critical inverse temperature 1/θ, while worst-case mixing is exponential in N with rate equal to the free-energy difference between spiked and null models.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Langevin dynamics for large-signal spiked matrices mix in O(log N) from uniform spherical starts even below the critical temperature.","strongest_claim":"Initialized from the uniform-at-random spherical prior, the mixing time in the low-temperature α>1 regime is O(log N). 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