Skip to main content
SpringerLink
Log in

Boolean Functions with Small Second-Order Influences on the Discrete Cube

  • Conference paper
  • First Online:
High Dimensional Probability IX

Part of the book series: Progress in Probability ((PRPR,volume 80))

  • 265 Accesses

Abstract

Motivated by a recent paper of Tanguy (J Theoret Probab 33:692–714, 2020), in which the concept of second-order influences on the discrete cube and Gauss space has been investigated in detail, the present note studies it in a more specific context of Boolean functions on the discrete cube. Some bounds that Tanguy obtained in Tanguy (J Theoret Probab 33:692–714, 2020) as applications of his more general approach are extended and complemented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Bonami, Étude des coefficients Fourier des fonctions de Lp(G). Ann. Inst. Fourier 20, 335–402 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Friedgut, G. Kalai, A. Naor, Boolean functions whose Fourier transform is concentrated on the first two levels. Adv. Appl. Math. 29, 427–437 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Harper, Optimal assignments of numbers to vertices. J. Soc. Ind. Appl. Math. 12, 131–135 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Kahn, G. Kalai, N. Linial, The influence of variables on Boolean functions, in Proceedings of 29th Annual Symposium on Foundations of Computer Science, vol. 62 (Computer Society Press, Washington, 1988), pp. 68–80

    Google Scholar 

  5. T. Przybyłowski, Influences of higher orders in the Boolean analysis. Master’s thesis, University of Warsaw (2022)

    Google Scholar 

  6. K. Tanguy, Talagrand inequality at second order and application to Boolean analysis. J. Theoret. Probab. 33, 692–714 (2020)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Research supported by the National Science Centre, Poland, project number 2015/18/A/ST1/00553.

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Krzysztof Oleszkiewicz

Authors
  1. Krzysztof Oleszkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krzysztof Oleszkiewicz .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Warszawa, Poland

    Radosław Adamczak

  2. MAP5, Université Paris Cité, Paris, France

    Nathael Gozlan

  3. Centre de Mathématiques Appliquées, École Polytechnique, Palaiseau, France

    Karim Lounici

  4. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Mokshay Madiman

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Oleszkiewicz, K. (2023). Boolean Functions with Small Second-Order Influences on the Discrete Cube. In: Adamczak, R., Gozlan, N., Lounici, K., Madiman, M. (eds) High Dimensional Probability IX. Progress in Probability, vol 80. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-26979-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation