Limit theorems for the alloy-type random energy model

In this paper, we consider limit laws for the model, which is a generalization of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, while the second has the mean na with some a∈R, and the variance σ≠1. The phase space (a,σ)⊂R×R+ is divided into several...