Spherically symmetric random permutations

We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group Sn and are consistent as n varies. The extreme infinitely spherically symmetric permutation-valued processes are identified for the Hamming, Kendall-tau and Cayley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity.NSF (grant DMS-1407562)NSF (grant DMS‐1664619