Fast initial conditions for Glauber dynamics

Eyal Lubetzky, Allan Sly

Research output: Contribution to journalArticlepeer-review

Abstract

In the study of Markov chain mixing times, analysis has centered on the performance from a worst-case starting state. Here, in the context of Glauber dynamics for the one-dimensional Ising model, we show how new ideas from information percolation can be used to establish mixing times from other starting states. At high temperatures we show that the alternating initial condition is asymptotically the fastest one, and, surprisingly, its mixing time is faster than at infinite temperature, accelerating as the inverse-temperature β ranges from 0 to β0=12arctanh(13). Moreover, the dominant test function depends on the temperature: at β< β it is autocorrelation, whereas at β> β it is the Hamiltonian.

Original languageEnglish (US)
Pages (from-to)647-667
Number of pages21
JournalProbability Theory and Related Fields
Volume181
Issue number1-3
DOIs
StatePublished - Nov 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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