The expected number of inversions after n adjacent transpositions
arXiv:0909.0103 · doi:10.1016/j.disc.2004.09.015
Abstract
We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane.