Open Access
2008 On differentiability of the Parisi formula
Dmitry Panchenko
Author Affiliations +
Electron. Commun. Probab. 13: 241-247 (2008). DOI: 10.1214/ECP.v13-1365


It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of the differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.


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Dmitry Panchenko. "On differentiability of the Parisi formula." Electron. Commun. Probab. 13 241 - 247, 2008.


Accepted: 4 May 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1205.82092
MathSciNet: MR2399285
Digital Object Identifier: 10.1214/ECP.v13-1365

Primary: 60K35
Secondary: 82B44

Keywords: Parisi formula , Sherrington-Kirkpatrick model

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