Expected length of a product of random reflections

Jonas Sjostrand

Expected length of a product of random reflections

Combinatorics 2010-11-25 v1

Authors: Jonas Sjostrand

Abstract

We present a simple formula for the expected number of inversions in a permutation of size $n$ obtained by applying $t$ random (not necessarily adjacent) transpositions to the identity permutation. More general, for any finite irreducible Coxeter group belonging to one of the infinite families (type A, B, D, and I), an exact expression is obtained for the expected length of a product of $t$ random reflections.

Keywords

random reflections Coxeter groups expected length inversions transpositions permutations

Cite

@article{arxiv.1011.5358,
  title  = {Expected length of a product of random reflections},
  author = {Jonas Sjostrand},
  journal= {arXiv preprint arXiv:1011.5358},
  year   = {2010}
}

Comments

11 pages

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