Stein's method, semicircle distribution, and reduced decompositions of   the longest element in the symmetric group
  Consider a uniformly chosen random reduced decomposition of the longest element in the symmetric group. It is known that the location of the first transposition in this decomposition converges to the semicircle distribution. In this note we provide a sharp error term for this result, using the "comparison of generators" approach to Stein's method. 
Jason Fulman and Larry Goldstein
math.PR math.CO