Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 12 (2007), paper no. 38, 401-410.
A note on Talagrand's positivity principle
Talagrand's positivity principle states that one can slightly perturb a Hamiltonian in the Sherrington-Kirkpatrick model in such a way that the overlap of two configurations under the perturbed Gibbs' measure will become typically nonnegative. In this note we observe that abstracting from the setting of the SK model only improves the result and does not require any modifications in Talagrand's argument. In this version, for example, positivity principle immediately applies to the setting of replica symmetry breaking interpolation. Also, abstracting from the SK model improves the conditions in the Ghirlanda-Guerra identities and as a consequence results in a perturbation of smaller order necessary to ensure positivity of the overlap.
Electron. Commun. Probab., Volume 12 (2007), paper no. 38, 401-410.
Accepted: 21 October 2007
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
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Panchenko, Dmitriy. A note on Talagrand's positivity principle. Electron. Commun. Probab. 12 (2007), paper no. 38, 401--410. doi:10.1214/ECP.v12-1326. https://projecteuclid.org/euclid.ecp/1465224981