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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 16 open journal systems 


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.


Full text: PDF

Pages: 155-166

Published on: July 22, 2005
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Electronic Communications in Probability. ISSN: 1083-589X