Error bounds in normal approximation for the squared-length of total spin in the mean field classical $N$-vector models

Electronic Communications in Probability

Lê Vǎn Thành¹ 

关键词: Stein’s method;    Kolmogorov distance;    Wasserstein distance;    mean-field model;   

DOI  :  10.1214/19-ECP218

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY