Randomly growing braid on three strands and the Manta ray

• 成果类型: Article
• 署名作者: Mairesse, Jean; Matheus, Frederic
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000754
• 发表日期: 2007
• 页码: 502-536
• 关键词: random-walks; GROWTH

摘要

Consider the braid group B-3 = < a, b vertical bar aba = bab > and the nearest neighbor random walk defined by a probability v with support {a, a(-1), b, b(-1)}. The rate of escape of the walk is explicitly expressed in function of the unique solution of a set of eight polynomial equations of degree three over eight indeterminates. We also explicitly describe the harmonic measure of the induced random walk on B-3 quotiented by its center. The method and results apply, mutatis mutandis, to nearest neighbor random walks on dihedral Artin groups.