A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximat...A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.展开更多
基金supported by Hong Kong Research Grants Council General Research Fund (Grant Nos. 403513 and 14302515)
文摘A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.
