Electronic Communications in Probability

On the accuracy of the normal approximation for the free energy in the Random Energy Model

Raphael Meiners and Anselm Reichenbachs

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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.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 12, 11 pp.

Accepted: 12 February 2013
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Random Energy Model free energy moderate deviations large deviations

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Meiners, Raphael; Reichenbachs, Anselm. On the accuracy of the normal approximation for the free energy in the Random Energy Model. Electron. Commun. Probab. 18 (2013), paper no. 12, 11 pp. doi:10.1214/ECP.v18-2377. https://projecteuclid.org/euclid.ecp/1465315551

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