A Central Limit Theorem for Weighted Averages of Spins in the High Temperature Region of the Sherrington-Kirkpatrick Model

Dmitry Panchenko (Massachusetts Institute of Technology, USA)

Abstract


In this paper we prove that in the high temperature region of the Sherrington-Kirkpatrick model for a typical realization of the disorder the weighted average of spins $\sum_{i \leq N} t_i \sigma_i$ will be approximately Gaussian provided that $\max_{i \leq N}|t_i|/\sum_{i \leq N} t_i^2$ is small.

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Pages: 499-524

Publication Date: June 13, 2005

DOI: 10.1214/EJP.v10-258

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