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A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington-Kirkpatrick model

Research paper by Dmitry Panchenko

Indexed on: 18 May '04Published on: 18 May '04Published in: Mathematics - Probability



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.