Random number theory and real analytic probability

在我们的项目之前，已经证明了几乎所有的无理旋转的依赖性消失时，它适用于Rademacher函数的中心极限定理。这一结果解释了为什么在高维空间中，拟Monte Carlo方法与普通Monte Carlo方法相比不起作用，针对这一结果，我们对无理旋转进行了分类，并详细研究了产生序列收敛于相依平稳序列的无理旋转。给出了极限序列独立的条件，成功地得到了证明极限独立性的数值有效方法，证明了多重n元变换的中心极限定理。这一结果与利用多重变换产生随机数的accuracy理论密切相关。

Before our project, it had been proved that dependence of almost all irrational rotation vanish when it applied for the central limit theorem of Rademacher functions. This result explains why the quasi Monte Carlo methods are not effective in high dimensional space comparing with the ordinary Monte Carlo method.Concerning this result, we classified irrational rotations and studied in detail on irrational rotations which generate the sequence converges to dependent stationary sequence. We have given conditions to have independent limit sequence and succeeded to have the numerically effective mean to verify the independence of limit.We prove the central limit theorem for multiple n-ary transforms. This results is closely related to the theory of accelation of generation of random numbers by means of multiple transforms.