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.

Source : oai:HAL:hal-00412143v1

Volume: Vol. 12 no. 2

Published on: August 31, 2009

Submitted on: March 26, 2015

Keywords: Permutations,Markov chains,inversions,05A05, 05A15, 05A16, 60J10,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]

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