• Corpus ID: 218487492

Fluctuations in Mean-Field Ising models

@article{Deb2020FluctuationsIM,
  title={Fluctuations in Mean-Field Ising models},
  author={Nabarun Deb and Sumit Mukherjee},
  journal={arXiv: Probability},
  year={2020}
}
In this paper, we study the fluctuations of the average magnetization in an Ising model on an approximately $d_N$ regular graph $G_N$ on $N$ vertices. In particular, if $G_N$ is \enquote{well connected}, we show that whenever $d_N\gg \sqrt{N}$, the fluctuations are universal and same as that of the Curie-Weiss model in the entire Ferro-magnetic parameter regime. We give a counterexample to demonstrate that the condition $d_N\gg \sqrt{N}$ is tight, in the sense that the limiting distribution… 

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  • Computer Science
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