Cutoff for conjugacy-invariant random walks on the permutation group

@article{Berestycki2014CutoffFC,
  title={Cutoff for conjugacy-invariant random walks on the permutation group},
  author={N. Berestycki and Batı Şeng{\"u}l},
  journal={Probability Theory and Related Fields},
  year={2014},
  volume={173},
  pages={1197-1241}
}
  • N. Berestycki, Batı Şengül
  • Published 2014
  • Mathematics
  • Probability Theory and Related Fields
  • We prove a conjecture raised by the work of Diaconis and Shahshahani (Z Wahrscheinlichkeitstheorie Verwandte Geb 57(2):159–179, 1981) about the mixing time of random walks on the permutation group induced by a given conjugacy class. To do this we exploit a connection with coalescence and fragmentation processes and control the Kantorovich distance by using a variant of a coupling due to Oded Schramm as well as contractivity of the distance. Recasting our proof in the language of Ricci curvature… CONTINUE READING
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