演講者： 黃皓瑋 教授 (國立中山大學應用數學系)
標題：Limit Theorems in the Hadamard Products of Random Matrix Ensembles
地點：校本部第二綜合大樓8樓 B808 教室
摘要： In Wigner's seminal work, he established that the empirical spectral distribution of certain types of random matrix ensembles converges to the Wigner's semicircular law named after him when the dimension goes to infinity. Since the invention of free probability theory, several asymptotic free phenomena have been discovered for a wider range of random matrix ensembles. On the other hand, in nuclear physics, a system that is not of full connectivity can be described by sparse random matrix ensembles, and these matrices can be further expressed in terms of Hadamard products. Recently, the limit theorem of the Hadamard product of Wigner random matrices was derived based on combinatorial strategy. However, some issues related to this topic are remaining open, such as the lack of analytic proof for Wigner types and the asymptotic behavior of the Hadamard product of Wishart types. In this talk, we will first offer a brief introduction to random matrix theory and then mention its association to other fields. In the end, some other relevant topics and the latest developments will be addressed.