We derive upper and lower bounds for the spectral gap of the random
energy model under Metropolis dynamics which are sharp in exponential order.
They are based on the variational characterization of the gap. For the lower
bound, a Poincaré inequality derived by Diaconis and Stroock is used. The
scaled asymptotic expression is a linear function of the temperature. The
corresponding function for a global version of the dynamics exhibits phase
transition instead.
¶ We also study the dependence of lower order terms on the volume. In
the global dynamics, we observe a phase transition. For the local dynamics, the
expressions we have, which are possibly not sharp, do not change their order of
dependence on the volume as the temperature changes.
Publié le : 1998-08-14
Classification:
Disordered systems,
spin glasses,
random energy model,
Metropolis dynamics,
Glauber dynamics,
convergence to equilibrium,
spectral gap,
dynamical phase transition,
60K35,
82B44
@article{1028903457,
author = {Fontes, L. R. G. and Isopi, M. and Kohayakawa, Y. and Picco, P.},
title = {The spectral gap of the REM under Metropolis dynamics},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 917-943},
language = {en},
url = {http://dml.mathdoc.fr/item/1028903457}
}
Fontes, L. R. G.; Isopi, M.; Kohayakawa, Y.; Picco, P. The spectral gap of the REM under Metropolis dynamics. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 917-943. http://gdmltest.u-ga.fr/item/1028903457/