Central limit theorems for Coxeter systems and Artin systems of extra large type

2003/11/06 by Gero Fendler, gero Fendler, Fendler, gero · 1 citation
Mathematics · #46L53 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Random Matrices and Applications #math.FA #msc:46L53

paper · pdf · doi:10.48550/arxiv.math/0311076

12 pages

arxiv created 2003/11/06 · openalex publication_date 2003/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a Coxeter system of large type we prove a non--commutative central limit theorem: After normalisation with the square root of n the characteristic function of the set of the first n generators tends in distribution to Wigners semi--circle law. If one chooses the group presentation at random, now admitting a certain amount of commutation among the generators, the distributional limit will be the q--deformed semi--circle law, 1≤ q ≤ 1, almost surely.

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