A Proof of Walsh's Convergence Theorem Using Couplings
A Proof of Walsh's Convergence Theorem Using Couplings
复制标题
用耦合证明沃尔什收敛定理
DOI：
10.1093/imrn/rnu145
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发表时间：
2013
影响因子：
1
通讯作者：
Tim Austin
中科院分区：
文献类型：
--
作者：
Tim Austin
沃尔什最近证明了离散幂零作用群中所有涉及多项式序列的非常规遍历平均的范数收敛性。他推导出这种收敛从一个等价的，“有限”断言的稳定性在任意长的时间间隔，这些平均值，这是证明了基本上有限的手段。本论文展示了如何感应的核心沃尔什的证明也可以实现使用更经典的概念遍历理论：特别是，耦合和特征因子。
Walsh has recently proved the norm convergence of all nonconventional ergodic averages involving polynomial sequences in discrete nilpotent acting groups. He deduces this convergence from an equivalent, `finitary' assertion of stability over arbitrarily long time-intervals for these averages, which is proved by essentially finitary means. The present paper shows how the induction at the heart of Walsh's proof can also be implemented using more classical notions of ergodic theory: in particular, couplings and characteristic factors.