A Question about the Parisi Functional

Dmitriy Panchenko (Massachusetts Institute of Technology, USA)

Abstract


We conjecture that the Parisi functional in the SK model is convex in the functional order parameter and prove a partial result that shows the convexity along one-sided directions. A consequence of this result is the log-convexity of $L_m$ norm for a class or random variables.

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Pages: 155-166

Publication Date: July 22, 2005

DOI: 10.1214/ECP.v10-1145

References


    1. Guerra, Francesco. Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys. 233 (2003), no. 1, 1--12. MR1957729

    2.     Sherrington D., Kirkpatrick S. Solvable model of a spin glass. Phys. Rev. Lett. 35 (1972), 1792--1796.

    3.     Talagrand, Michel. Spin glasses: a challenge for mathematicians. Cavity and mean field models. Springer-Verlag, Berlin, 2003. x+586 pp. ISBN: 3-540-00356-8 MR1993891

    4. Talagrand, Michel. The generalized Parisi formula. C. R. Math. Acad. Sci. Paris 337 (2003), no. 2, 111--114. MR1998841

    5. Talagrand, Michel. Parisi formula. To appear in Ann. Math.

    6. Talagrand, Michel. On the meaning of Parisi's functional order parameter. C. R. Math. Acad. Sci. Paris 337 (2003), no. 9, 625--628. MR2017738

    7. Talagrand, Michel. Parisi measures. Preprint.
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