# Details of talk

Title | Trimmed sums for observables on the doubling map |
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Presenter | Tanja Schindler (Australian National University) |

Author(s) | Tanja Schindler |

Session | Dynamical Systems and Fluid Dynamics |

Time | 14:30:00 2017-09-25 |

Abstract | For measure preserving ergodic dynamical systems there is no strong law of large numbers if the expectation has infinite mean. In some cases it is possible to obtain a generalised strong law of large numbers by deleting the maximum entry, for examples for the digits of a continued fraction expansion. Haynes proved that there is no strong law of large numbers by only deleting a finite number of terms (light trimming) on iterations of the doubling map with observable $1/x$, eventhough this would be possible if one considered independent random variables with the same distribution function. Based on this result Haynes and myself have shown that a strong law does still hold in this case depending if for the number of deleted terms $b_n$ of the sum of the first $n$ entries it holds that $\lim_{n\to\infty}b_n/\log\log\log n=\infty$ or not. |