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}
}
Comments
22 pages