A mathematical reformulation of Derrida's REM and GREM
The author investigates two statistical models introduced by \textit{B. Derrida} and called respectively random energy model (REM) [Random-energy model: Limit of a family of disordered models, Phys. Rev. Lett. 45, 79-82 (1982), and Random-energy model: An exactly solvable model of disordered systems, Phys. Rev. B 24, 2613-2626 (1981)] and general random energy model (GREM) [A generalization of the random energy model which includes correlations between energies, J. Phys. Lett. 46, L401-L407 (1985), and \textit{B. Derrida} and \textit{E. Gardner}, Solution of the generalized random energy model, J. Phys. C, in press (1986)]. In Derrida's original formulation of the REM and GREM certain limits are implicit. By means of a modification of the Poisson distribution on the corresponding configurational space the author gives a mathematical reformulation where these limits have already been taken. It permits for instance to perform more systematic calculations of relevance to Parisi's solution of the Sherrington-Kirkpatrick spin-glass model.
scientific article; zbMATH DE number 4001167