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

[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.

[学科分类] 统计和概率

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