Cut-off phenomenon for random walks on free orthogonal quantum groups

• 成果类型: Article
• 署名作者: Freslon, Amaury
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0863-8
• 发表日期: 2019
• 页码: 731-760
• 关键词: symmetries

摘要

We give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups. As a consequence, we prove that the analogue of the uniform plane Kac walk on this quantum group has a cut-off at Nln(N)/2(1-cos(theta)). This is the first result of this type for genuine compact quantum groups. We also obtain similar results for mixtures of rotations and quantum permutations.