6月14日,美国明尼苏达大学姜铁锋教授(Distributions of Angles in Random Packing on Spheres)
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报告题目:Distributions of Angles in Random Packing on Spheres

报告时间:201761414:00-17:00

报告地点:对外经济贸易大学诚信楼715

主办学院:统计学院

报告专家:

姜铁锋,美国明尼苏达大学的终身教授,主要从事概率统计理论及其相关领域的研究,特别是在概率论、高维统计学以及纯数学等交叉学科取得了突破性的进展。姜教授开创的随机几何领域中球面上随机点的研究结果还被德国慕尼黑大学物理学家Daniel Junghans应用在宇宙大爆炸理论的研究之中。除获得多次美国自然科学基金外,还获得2005年的美国总统奖。姜教授目前已发表论文30多篇,其中绝大部分发表在国际顶尖的概率统计与机器学习杂志上,包括《Ann. Probab.5篇,《Probab. Theor. Rel. Fields3篇,《Ann. Stat.2篇,《Ann. Appl. Probab.2篇,《Journal of Machine Learning Research1篇等等。另外更百余次在重要国际会议和世界著名大学做邀请报告、组织学术会议、开展暑期研讨班的教学。

报告内容简介:

We will consider the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in the p-dimensional Euclidean spaces as the number of points n goes to infinity, while the dimension pis either fixed or growing with n. For both settings, we derive the limiting empirical distribution of the random angles and the limiting distributions of the extreme angles. The results reveal interesting differences in the two settings and provide a precise characterization of the folklore that all high-dimensional random vectors are almost always nearly orthogonal to each other. Applications to statistics and machine learning and connections with some open problems in physics and mathematics are also discussed. This is a join work with Tony Cai and Jianqing Fan.