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摘要翻译：
研究了无穷测度动力系统中某些观测函数时间平均的极限定理。Rayleigh-Benard对流和Belousov-Zhabotinsky反应等间歇现象是用无穷测度动力系统描述的，我们证明了不是$L^1(m)$函数的观测函数的时间平均值收敛于广义反正弦分布，其关于不变测度$m$的平均值是有限的。这一结果导致了新的观点，即相关函数本质上是随机的，不会衰减。数值计算表明，当观测函数具有无穷大均值时，观测函数的时间平均值收敛于稳定分布。
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英文标题：
《Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical
System》
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作者：
Takuma Akimoto
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.
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PDF链接：
https://arxiv.org/pdf/801.1382
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