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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Optimal condition for asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation
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by Jan Haskovec and Mauro Rodriguez Cartabia
Proc. Amer. Math. Soc. 151 (2023), 3871-3878
DOI: https://doi.org/10.1090/proc/16482
Published electronically: May 12, 2023

Abstract:

We prove that asymptotic global consensus is always reached in the Hegselmann-Krause model with finite speed of information propagation ${\mathfrak {c}}>0$ under minimal (i.e., necessary) assumptions on the influence function. In particular, we assume that the influence function is globally positive, which is necessary for reaching global consensus, and such that the agents move with speeds strictly less than ${\mathfrak {c}}$, which is necessary for well-posedness of solutions. From this point of view, our result is optimal. The proof is based on the fact that the state-dependent delay, induced by the finite speed of information propagation, is uniformly bounded.
References
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Bibliographic Information
  • Jan Haskovec
  • Affiliation: Computer, Electrical and Mathematical Sciences & Engineering, King Abdullah University of Science and Technology, 23955-6900 Thuwal, Kingdom of Saudi Arabia
  • MR Author ID: 754324
  • ORCID: 0000-0003-3464-304X
  • Email: jan.haskovec@kaust.edu.sa
  • Mauro Rodriguez Cartabia
  • Affiliation: IMAS (UBA-CONICET) and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • MR Author ID: 1293206
  • ORCID: 0000-0001-9689-8916
  • Email: mrodriguezcartabia@dm.uba.ar
  • Received by editor(s): July 28, 2022
  • Received by editor(s) in revised form: January 6, 2023
  • Published electronically: May 12, 2023
  • Communicated by: Wenxian Shen
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 3871-3878
  • MSC (2020): Primary 34K20, 34K60, 82C22
  • DOI: https://doi.org/10.1090/proc/16482
  • MathSciNet review: 4607631