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

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.