学术报告报告题目：Strong convergence for tensor GUE random matrices
报 告 人：袁望钧（南方科技大学）
报告时间：2025 年12月 23日（星期二）上午11:00-12:00
报告地点：37号楼3A02
邀 请 人：张纪元 副教授
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数学学院
2025年12月18日
报告摘要：
Haagerup and Thorbjørnsen (2005) proved that iid GUEs converge strongly to free semicircular elements as the dimension grows to infinity. Motivated by considerations from quantum physics – in particular, understanding nearest neighbor interactions in quantum spin systems – we consider iid GUE acting on multipartite state spaces, with components on some of the sites and identity on the remaining sites. In the case that the GUEs appear on more than half of the states, we show that under proper assumptions on the dimension of the sites, strong asymptotic freeness still holds. If the GUEs are allowed to be on the states without overlap, we believe that they are are strong asymptotic epsilon-free. Our proof relies on an interpolation technology recently introduced by Bandeira, Boedihardjo and van Handel (2023). This is a combination of a joint work with Benoit Collins.
报告人简介：
Wangjun Yuan is currently an assistant professor at Southern University of Science and Technology. He got a bachelor's degree in mathematics from University of Science and Technology of China in 2017, and then a Ph.D. degree in mathematics from The University of Hong Kong in 2021 under the supervision of Jian Song, Guangyue Han and Jianfeng Yao. After that, he has been a postdoc fellow at University of Ottawa supported by Raluca Balan from 2021 to 2022, and then a postdoc researcher at the University of Luxembourg working with Mark Podolskij beforing joining SUSTech.
His research interests are mainly in the field of random matrix theory, stochastic differential equation, stochastic partially differential equation and Malliavin calculus.