Geodesic
The expected number of inversions after n adjacent transpositions
Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2.

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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. 
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     author = {Bousquet-M\'elou, Mireille},
     title = {The expected number of inversions after n adjacent transpositions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     number = {2},
     year = {2010},
     doi = {10.46298/dmtcs.478},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.478/}
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Bousquet-Mélou, Mireille. The expected number of inversions after n adjacent transpositions. Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 2. doi : 10.46298/dmtcs.478. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.478/

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