- 97-135 Fontes L.R.G., Isopi M., Kohayakawa Y., Picco P.
- The Spectral Gap of the REM under Metropolis Dynamics
Mar 17, 97
(auto. generated ps),
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Abstract. 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 Poincar\'e
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.