Asymptotic behaviour of the conjugacy probability of the alternating group.

For G a finite group, κ(G) is the probability that σ, τ ∈ G are conjugate, when σ and τ are chosen independently and uniformly at random. Recently, Blackburn et al. (J Lond Math Soc 86(2):755-778, 2012) gave an elementary proof that κ (S_n) ~ A/n² as n → ∞ for some constant A--a result which was first proved by Flajolet et al. (Electron J Comb 13(1):35, 2006). In this paper, we extend the elementary methods of Blackburn et al. to show that κ(A_n) ~ B/n² as n → ∞ for some constant B, given explicitly in this paper. [ABSTRACT FROM AUTHOR]