Abstract
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.
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References
G. Amir and O. Gurel-Gurevich: The diameter of a random Cayley graph of Zq, Groups Complex. Cryptol.2 (2010), 59–65.
L. Clozel, H. Oh and E. Ullmo: Hecke operators and equidistribution of Hecke points, Invent. Math.144 (2001), 327–351.
M. Einsiedler, S. Mozes, N. Shah and U. Shapira: Equidistribution of primitive rational points on expanding horospheres, Compos. Math.152 (2016), 667–692.
A. Eskin and H. Oh: Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems26 (2006), 163–167.
D. Goldstein and A. Mayer: On the equidistribution of Hecke points, Forum Math.15 (2003), 165–189.
J. Marklof: The asymptotic distribution of Frobenius numbers, Invent. Math.181 (2010), 179–207.
J. Marklof and A. Strömbergsson: Diameters of random circulant graphs, Combinatorica33 (2013), 429–466.
H. P. F. Swinnerton-Dyer: A brief guide to algebraic number theory, London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 50, 2001.
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Shapira, U., Zuck, R. Asymptotic Metric Behavior of Random Cayley Graphs of Finite Abelian Groups. Combinatorica 39, 1133–1148 (2019). https://doi.org/10.1007/s00493-017-3672-2
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DOI: https://doi.org/10.1007/s00493-017-3672-2