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- W2785755052 abstract "In this paper, we consider limit laws for the model, which is a generalisation 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 (sqrt{n}a) with some (ain R,) and the variance (sigma ne 1). The phase space ((a,sigma) subset R times R_+) is divided onto several domains, where after appropriate normalisation, the partition function converges in law to the stable distribution. These domains are separated by the critical surfaces, corresponding to transitions from the normal distribution to (alpha-)stable with (alpha in (1,2)), after to 1-stable, and finally to (alpha-)stable with (alpha in (0,1).) The corresponding phase diagram is the central result of this paper." @default.
- W2785755052 created "2018-02-23" @default.
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- W2785755052 date "2018-02-14" @default.
- W2785755052 modified "2023-09-27" @default.
- W2785755052 title "Limit Theorems for the Alloy-type Random Energy Model" @default.
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