## 抄録

In infinite ergodic theory, two distributional limit theorems are well-known. One is characterized by the Mittag-Leffler distribution for time averages of L^{1}(m) functions, i.e., integrable functions with respect to an infinite invariant measure. The other is characterized by the generalized arc-sine distribution for time averages of non-L^{1}(m) functions. Here, we provide another distributional behavior of time averages of non-L^{1}(m) functions in one-dimensional intermittent maps where each has an indifferent fixed point and an infinite invariant measure. Observation functions considered here are non-L^{1}(m) functions which vanish at the indifferent fixed point. We call this class of observation functions weak non-L^{1}(m) function. Our main result represents a first step toward a third distributional limit theorem, i.e., a distributional limit theorem for this class of observables, in infinite ergodic theory. To prove our proposition, we propose a stochastic process induced by a renewal process to mimic a Birkoff sum of a weak non-L^{1}up>(m) function in the one-dimensional intermittent maps.

本文言語 | English |
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ページ（範囲） | 476-493 |

ページ数 | 18 |

ジャーナル | Journal of Statistical Physics |

巻 | 158 |

号 | 2 |

DOI | |

出版ステータス | Published - 2015 1月 1 |

## ASJC Scopus subject areas

- 統計物理学および非線形物理学
- 数理物理学

## フィンガープリント

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