Measure complexity and Möbius disjointness

Wen Huang; Zhiren Wang; Xiangdong Ye

doi:10.1016/j.aim.2019.03.007

Measure complexity and Möbius disjointness

Wen Huang, Zhiren Wang, Xiangdong Ye

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's Möbius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity. We then apply this result to a number of situations, including certain systems whose invariant measure don't all have discrete spectrum.

Original language	English (US)
Pages (from-to)	827-858
Number of pages	32
Journal	Advances in Mathematics
Volume	347
DOIs	https://doi.org/10.1016/j.aim.2019.03.007
State	Published - Apr 30 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2019.03.007

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abstract = "In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's M{\"o}bius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity. We then apply this result to a number of situations, including certain systems whose invariant measure don't all have discrete spectrum.",

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N2 - In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's Möbius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity. We then apply this result to a number of situations, including certain systems whose invariant measure don't all have discrete spectrum.

AB - In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's Möbius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity. We then apply this result to a number of situations, including certain systems whose invariant measure don't all have discrete spectrum.

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JO - Advances in Mathematics

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Measure complexity and Möbius disjointness

Abstract

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