Abstract
This paper gives the Kolmogorov and Wasserstein bounds in normal approximation for the squared-length of total spin in the mean field classical $N$-vector models. The Kolmogorov bound is new while the Wasserstein bound improves a result obtained recently by Kirkpatrick and Nawaz [Journal of Statistical Physics, 165 (2016), no. 6, 1114–1140]. The proof is based on Stein’s method for exchangeable pairs.
Citation
Lê Vǎn Thành. Nguyen Ngoc Tu. "Error bounds in normal approximation for the squared-length of total spin in the mean field classical $N$-vector models." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP218
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