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Higher Order Correlations for Group Actions

  • Alexander GorodnikEmail author
Chapter
Part of the Infosys Science Foundation Series book series (ISFS)

Abstract

This survey paper discusses behaviour of higher order correlations for one-parameter dynamical systems and more generally for dynamical systems arising from group actions. In particular, we present a self-contained proof of quantitative bounds for higher order correlations of actions of simple Lie groups. We also outline several applications of our analysis of correlations that include asymptotic formulas for counting lattice points, existence of approximate configurations in lattice subgroups, and validity of the Central Limit Theorem for multiparameter group actions.

Notes

Acknowledgements

This survey paper has grown out of the lecture series given by the author at the Tata Institute of Fundamental Research in Spring 2017. I would like to express my deepest gratitude to the Tata Institute for the hospitality and to the organisers of this programme—Shrikrishna Dani and Anish Ghosh—for all their hard work on setting up this event and making it run smoothly. I also would like to thank the referee for carefully reading the draft and for his thoughtful comments.

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Authors and Affiliations

  1. 1.University of ZurichZurichSwitzerland

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