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Fluctuations in Derrida's random energy and generalized random energy models |
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| Authors: | Antonio Galves Servet Martinez Pierre Picco |
| Institution: | (1) Centre de Physique Théorique (Laboratoire Propre, LP7061), CNRS-Luminy-Case 907, F-13288 Marseille, France;(2) Universidade de São Paulo, São Paulo, Brazil;(3) Universidad de Chile, Santiago, Chile |
| 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. |
| Keywords: | Random energy random variables finite-size corrections Poisson point process |
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