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Convergence Time to Equilibrium of the Metropolis dynamics for the GREM

Probability 2020-01-08 v1

Abstract

We study the convergence time to equilibrium of the Metropolis dynamics for the Generalized Random Energy Model with an arbitrary number of hierarchical levels, a finite and reversible continuous-time Markov process, in terms of the spectral gap of its transition probability matrix. This is done by deducing bounds to the inverse of the gap using a Poincar\'e inequality and a path technique. We also apply convex analysis tools to give the bounds in the most general case of the model.

Keywords

Cite

@article{arxiv.1907.00436,
  title  = {Convergence Time to Equilibrium of the Metropolis dynamics for the GREM},
  author = {A. M. B. Nascimento and L. R. Fontes},
  journal= {arXiv preprint arXiv:1907.00436},
  year   = {2020}
}

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22 pages