Low-temperature Ising dynamics with random initializations

Glauber dynamics on spin systems are well known to suffer exponential slowdowns at low temperatures due to the emergence of multiple metastable phases, separated by narrow bottlenecks that are hard for the dynamics to cross. It is a folklore belief that if the dynamics is initialized from an appropriate random mixture of ground states, one for each phase, then convergence to the Gibbs distribution should be much faster. However, such phenomena have largely evaded rigorous analysis, as most tools in the study of Markov chain mixing times are tailored to worst-case initializations.