Abstract
In Černý and Wassmer (Probab. Theory Relat. Fields 167:253–303, 2017) [8], it was shown that the clock process associated with the Metropolis dynamics of the Random Energy Model converges to an \(\alpha \)-stable process, after being scaled by a random, Hamiltonian dependent, normalisation. We prove here that this random normalisation can be replaced by a deterministic one.
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Černý, J. (2019). Concentration of the Clock Process Normalisation for the Metropolis Dynamics of the REM. In: Gayrard, V., Arguin, LP., Kistler, N., Kourkova, I. (eds) Statistical Mechanics of Classical and Disordered Systems . StaMeClaDys 2018. Springer Proceedings in Mathematics & Statistics, vol 293. Springer, Cham. https://doi.org/10.1007/978-3-030-29077-1_5
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DOI: https://doi.org/10.1007/978-3-030-29077-1_5
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