On the cut-off phenomenon for the transitivity of randomly generated subgroups

@article{Galligo2012OnTC,
  title={On the cut-off phenomenon for the transitivity of randomly generated subgroups},
  author={Andr{\'e} Galligo and Laurent Miclo},
  journal={Random Struct. Algorithms},
  year={2012},
  volume={40},
  pages={182-219}
}
Consider K ≥ 2 independent copies of the random walk on the symmetric group SN starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time n ∈ N, let Gn be the subgroup of SN generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut-off phenomenon at time N ln(N)/(2K) for the non-existence of fixed point of Gn and for the transitivity of Gn… CONTINUE READING