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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 38 open journal systems 


A note on Talagrand's positivity principle

Dmitriy Panchenko, Massachusetts Institute of Technology, USA


Abstract
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.


Full text: PDF

Pages: 401-410

Published on: October 21, 2007
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Electronic Communications in Probability. ISSN: 1083-589X