| Abstract: | We study the random walk on the symmetric group (S_n) generated by the conjugacy class of cycles of length k. We show that the convergence to uniform measure of this walk has a cut-off in total variation distance after (frac{n}{k}log n) steps, uniformly in (k = o(n)) as (n rightarrow infty ). The analysis follows from a new asymptotic estimation of the characters of the symmetric group evaluated at cycles. |
