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Rényi 100, Quantitative and qualitative (in)dependence

Abstract

We discuss recent developments in the following important areas of Alfréd Rényi’s research interest: axiomatization of quantitative dependence measures, qualitative independence in combinatorics, conditional qualitative independence in statistics/data science and in measure theory/probability theory, and finally, prime gaps that are responsible for Rényi’s early career reputation. Most authors of this paper are main contributors to the new developments.

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Correspondence to T. F. Móri.

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We dedicate this paper to the memory of Alfréd Rényi who was born on March 20, 1921 and died on February 1, 1970 at the age of 49. He is the founding father of modern probability theory, information theory, and mathematical statistics in Hungary.

Supported by the Hungarian National Research, Development and Innovation Office (NKFIH) grants No. K119528 and KKP133819 to JP, K125569 to TFM.

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Arató, M., Katona, G.O.H., Michaletzky, G. et al. Rényi 100, Quantitative and qualitative (in)dependence. Acta Math. Hungar. 165, 218–273 (2021). https://doi.org/10.1007/s10474-021-01164-4

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Key words and phrases

  • axioms of dependence measures
  • qualitative independence
  • conditional qualitative independence
  • prime gaps

Mathematics Subject Classification

  • primary 00-02
  • secondary 05D05
  • 11N05
  • 60E05
  • 62H15
  • 62H17
  • 62H20