Near-linear-time weak recovery by Glauber dynamics

In the spiked Wigner inference problem, let annealed Glauber dynamics refer to the Markov chain studied in the paper, and let weak recovery mean achieving nonzero correlation with the planted signal. Glauber dynamics' runtime conjecture. Glauber dynamics succeeds at weak recovery in (near-)linear runtime. This conjecture is motivated by physics heuristics and rigorous results suggesting that the dynamics can achieve nonzero correlation in $O(N)$ steps, whereas the paper's current local-stationarity transfer techniques incur a polynomial overhead.