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2019 Error bounds in normal approximation for the squared-length of total spin in the mean field classical $N$-vector models
Lê Vǎn Thành, Nguyen Ngoc Tu
Electron. Commun. Probab. 24(none): 1-12 (2019). DOI: 10.1214/19-ECP218

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

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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

Information

Received: 5 July 2018; Accepted: 16 February 2019; Published: 2019
First available in Project Euclid: 22 March 2019

zbMATH: 1412.60046
MathSciNet: MR3933040
Digital Object Identifier: 10.1214/19-ECP218

Subjects:
Primary: 60F05

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