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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