scholarly journals Central limit theorem for fluctuations in the high temperature region of the Sherrington–Kirkpatrick spin glass model

2002 ◽  
Vol 43 (12) ◽  
pp. 6224-6237 ◽  
Author(s):  
Francesco Guerra ◽  
Fabio Lucio Toninelli
Keyword(s):  
High Temperature ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Spin Glass ◽  
Central Limit ◽  
Temperature Region ◽  
Spin Glass Model ◽  
High Temperature Region ◽  
Glass Model

scholarly journals Local Central Limit Theorem for Multi-group Curie–Weiss Models

2021 ◽  
Author(s):  
Michael Fleermann ◽  
Werner Kirsch ◽  
Gabor Toth
Keyword(s):  
High Temperature ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Temperature Regime ◽  
Mean Field ◽  
High Temperature Regime ◽  
The Mean ◽  
Local Central Limit Theorem ◽  
Group Version

AbstractWe study a multi-group version of the mean-field Ising model, also called Curie–Weiss model. It is known that, in the high-temperature regime of this model, a central limit theorem holds for the vector of suitably scaled group magnetisations, that is, for the sum of spins belonging to each group. In this article, we prove a local central limit theorem for the group magnetisations in the high-temperature regime.

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