# 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…

## 8 Citations

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- 2022

We continue our analysis of Ising models on the (directed) Erdős-Renyi random graph $G(N,p)$. We prove a quenched Central Limit Theorem for the magnetization and describe the fluctuations of the…

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We continue our analysis of Ising models on the (directed) Erdős–Rényi random graph. This graph is constructed on N vertices and every edge has probability p to be present. These models were…

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