Fluctuations for block spin Ising models

[摘要] We analyze the high temperature fluctuations of the magnetization of the so-called Ising block model. This model was recently introduced by Berthet et al. in [2]. We prove a Central Limit Theorems (CLT) for the magnetization in the high temperature regime. At the same time we show that this CLT breaks down at a line of critical temperatures. At this line we prove a non-standard CLT for the magnetization.

[学科分类] 统计和概率

[关键词] Ising model;Curie-Weiss model;fluctuations;Central Limit Theorem;block model