A note on Talagrand's positivity principle

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dc.creatorPanchenko, Dmitry
dc.date2007-08-18
dc.date.accessioned2026-07-07T08:37:14Z
dc.date.available2026-07-07T08:37:14Z
dc.descriptionTalagrand'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 Aizenman-Sims-Starr 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.
dc.identifierhttps://arxiv.org/abs/0708.2453
dc.identifierhttp://arxiv.org/abs/0708.2453
dc.identifierVol. 12 (2007) Elect. Comm. in Probab. 401-410
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140331
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B44
dc.titleA note on Talagrand's positivity principle
dc.typetext

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