Subadditive and multiplicative ergodic theorems
Subadditive and multiplicative ergodic theorems
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DOI：
10.4171/jems/958
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发表时间：
2020-01-01
影响因子：
2.6
通讯作者：
Karlsson, Anders
中科院分区：
文献类型：
--
作者：
Gouezel, Sebastien;Karlsson, Anders
证明了次加性遍历环的一个结果，提供了比Kingman次加性遍历定理更精细的信息。作为应用，我们推导了一个乘法遍历定理，推广了Karlsson-Ledrappier先前的一个结果，证明了半牵引力的随机乘积的增长总是由某个函数引导的。讨论了该结果在有界线性算子的遍历环、全纯映射和局部算子的遍历环上的应用，以及一个随机平均遍历定理。
A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of Karlsson-Ledrappier, showing that the growth of a random product of semicontractions is always directed by some horofunction. We discuss applications of this result to ergodic cocycles of bounded linear operators, holomorphic maps and topical operators, as well as a random mean ergodic theorem.