The Mixing Time for a Random Walk on the Symmetric Group Generated by Random Involutions
The Mixing Time for a Random Walk on the Symmetric Group Generated by Random Involutions
The involution walk is a random walk on the symmetric group generated by involutions with a number of 2-cycles sampled from the binomial distribution with parameter p. This is a parallelization of the lazy transposition walk onthesymmetricgroup.Theinvolutionwalkisshowninthispapertomixfor1 ≤p≤1fixed,nsufficientlylarge 2 in between log1/p(n) steps and log2/(1+p)(n) steps. The paper introduces a …