Uniform measures on braid monoids and dual braid monoids

JOURNAL OF ALGEBRA

卷:473

Article

Abbes, S.¹  Gouezel, S.²  Juge, V.^3,4  Mairesse, J.⁵ 

[1] Univ Paris Diderot, IRIF, UMR CNRS 8243, Paris, France

[2] Univ Nantes, CNRS, F-44035 Nantes, France

[3] Univ Paris Saclay, LSV, CNRS, LSV, Paris, France

[4] Univ Paris Saclay, ENS Cochran, Paris, France

[5] Univ Paris 06, Sorbonne Univ, CNRS, LIP6, 4 Pl Jussieu, F-75252 Paris 05, France

关键词: Positive braid monoid;    Birman-Ko-Lee dual braid monoid;    Uniform distribution;    Asymptotic properties;   

DOI  :  10.1016/j.jalgebra.2016.11.015

来源: Elsevier

【 摘 要 】

We aim at studying the asymptotic properties of typical positive braids, respectively positive dual braids. Denoting by ilk the uniform distribution on positive (dual) braids of length k, we prove that the sequence (mu(k))(k) converges to a unique probability measure mu(infinity) on infinite positive (dual) braids. The key point is that the limiting measure mu(infinity) has a Markovian structure which can be described explicitly using the combinatorial properties of braids encapsulated in the Mobius polynomial. As a by-product, we settle a conjecture by Gebhardt and Tawn (J. Algebra, 2014) on the shape of the Garside normal form of large uniform braids. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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