The expected number of inversions after n adjacent transpositions
Abstract
We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group Sm+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.
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