Asymptotic Metric Behavior of Random Cayley Graphs of Finite Abelian Groups

  • Uri ShapiraEmail author
  • Reut Zuck


Using methods of Marklof and Strömbergsson we establish several limit laws for metric parameters of random Cayley graphs of finite abelian groups with respect to a randomly chosen set of generators of a fixed size. Doing so we settle a conjecture of Amir and Gurel- Gurevich.

Mathematics Subject Classification (2000)

05C12 05C80 37A99 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Amir and O. Gurel-Gurevich: The diameter of a random Cayley graph of Zq, Groups Complex. Cryptol. 2 (2010), 59–65.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    L. Clozel, H. Oh and E. Ullmo: Hecke operators and equidistribution of Hecke points, Invent. Math. 144 (2001), 327–351.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. Einsiedler, S. Mozes, N. Shah and U. Shapira: Equidistribution of primitive rational points on expanding horospheres, Compos. Math. 152 (2016), 667–692.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A. Eskin and H. Oh: Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems 26 (2006), 163–167.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    D. Goldstein and A. Mayer: On the equidistribution of Hecke points, Forum Math. 15 (2003), 165–189.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J. Marklof: The asymptotic distribution of Frobenius numbers, Invent. Math. 181 (2010), 179–207.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. Marklof and A. Strömbergsson: Diameters of random circulant graphs, Combinatorica 33 (2013), 429–466.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    H. P. F. Swinnerton-Dyer: A brief guide to algebraic number theory, London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 50, 2001.Google Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTechnionHaifaIsrael

Personalised recommendations