The conjugacy character of \(S_ n\) tends to be regular (Q1100275)

For a finite group G, consider the conjugacy representation of G (i.e. the group algebra upon which the group acts by conjugation). Let \(\chi_ c\) denote the character of the conjugacy representation. In the paper under review \(\chi_ c\) is compared with the character \(\chi_ r\) of the regular representation (with respect to the standard inner product of class functions) when \(G=S_ n\), the symmetric group on n letters, and \(n\to \infty\). The authors prove that the angle between them tends to zero and the ratio of their norms tends to one as \(n\to \infty\).