Abstract
The fluctuations of the finite-size corrections to the free energy per site of the random energy model (REM) and the generalized random energy model (GREM) are investigated. Almost sure behavior for the corrections of order (logN)/N is given. We also prove convergence in distribution for the corrections of order 1/N.
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Galves, A., Martinez, S. & Picco, P. Fluctuations in Derrida's random energy and generalized random energy models. J Stat Phys 54, 515–529 (1989). https://doi.org/10.1007/BF01023492
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DOI: https://doi.org/10.1007/BF01023492