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Expected length of a product of random reflections

Authors
  • Sjostrand, Jonas
Type
Preprint
Publication Date
Nov 24, 2010
Submission Date
Nov 24, 2010
Identifiers
arXiv ID: 1011.5358
Source
arXiv
License
Yellow
External links

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.

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