论文标题
大国渐近学，Khinchin家庭和拉格朗日分布
Large Powers asymptotics, Khinchin families and Lagrangian distributions
论文作者
论文摘要
本文研究了Khinchin家族理论的多功能性，以进行渐近估计。我们表明，与晶格变量的局部中央限制定理相结合，Khinchin家族提供了一个方便而统一的框架，以处理大型功率序列系数的渐近结果。 我们在本文中从这个角度重新访问了这个经典主题，从而获得了清洁的新证明和许多新的结果。拉格朗日方程解决方案系数的渐近结果自然落入了该组合框架中。我们为拉格朗日概率分布家族的水獭和梅尔蒙渐近公式以及渐近结果提供了直接证明。
This paper delves on the versatility of the theory of Khinchin families for asymptotic estimation. We show that in combination with Local Central Limit theorems for lattice variables, Khinchin families furnish a convenient and unified framework to deal with asymptotic results of the coefficients of large powers of power series. We revisit in the present paper this classical theme from that point of view, obtaining clean new proofs and a number of new results. Asymptotic results for the coefficients of solutions of Lagrange's equation fall naturally into this combined framework. We provide a direct proof of an extension of the Otter and Meir-Moon asymptotic formula as well as asymptotic results for families of Lagrangian probability distributions.
