数学与统计学院学术报告[2023] 013号

(高水平大学建设系列报告784号)

报告题目: Asymptotics of Fredholm determinants associated with higher dimensional kernels

报告人：代丹

报告时间：2023年4月7日 16：00-17：00

报告地点：汇星楼501

报告内容：In this talk, we consider the Pearcey kernel and the hard edge Pearcey kernel, which appear in random matrix theory and many other stochastic models. They are viewed as higher dimensional kernels in the sense that they can be characterized by 3x3 matrix-valued Riemann-Hilbert problems. We establish integral representations for Fredholm determinants of integral operators with these kernels, which involve Hamiltonians associated with certain nonlinear differential equations. We also derive large gap asymptotics for the determinants and obtain asymptotic statistical properties for the related point processes.

报告人简历：代丹，香港城市大学副教授。研究兴趣主要包括渐近分析和随机矩阵等学术领域，在Advances in Mathematics，Communications in Mathematical Physics，SIAM Journal on Mathematical Analysis，Studies in Applied Mathematics，Nonlinearity等杂志发表多篇论文，并主持香港研究资助局多项研究项目。

                                               　数学与统计学院

                                                2023年04月06日