On the accuracy of the normal approximation for the free energy in the REM

Published 23 Dec 2012 in math.PR | (1212.5797v1)

Abstract: In the present paper we consider the fluctuations of the free energy in the random energy model (REM) on a moderate deviation scale. We find that for high temperatures the normal approximation holds only in a narrow range of scalings away from the CLT. For scalings of higher order, probabilities of moderate deviations decay faster than exponentially.

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