报告题目 (Title):Noncommutative logarithmic Sobolev inequalities
中文标题:非交换的对数Sobolev不等式
报告人 (Speaker):焦勇 教授(中南大学)
报告时间 (Time):2024年4月10日(周三) 10:00
报告地点 (Place):腾讯会议(514-885-492)
邀请人(Inviter):席东盟、李晋、张德凯、吴加勇
主办部门:古天乐代言太阳集团数学系
报告摘要:We show that the logarithmic Sobolev inequality holds for an arbitrary hypercontractive semigroup acting on a noncommutative probability space. Particularly, we can recover the p-logarithmic Sobolev inequality whenever the Riesz transform is bounded. Our inequality applies to numerous concrete cases, including Poisson semigroups for free groups, the Ornstein-Uhlenbeck semigroup for mixed Q-gaussian von Neumann algebras, the free product for Ornstein-Uhlenbeck semigroups etc. This provides a unified abstract approach to logarithmic Sobolev inequalities in noncommutative setting.