Expected length of a product of random reflections

2010/11/24 by Jonas Sjöstrand, Sjostrand, Jonas · 1 citation
Computer Science · Mathematics · #05A05 #60J10 #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1011.5358

openalex publication_date 2010/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Random braids and random walks on finite groups

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