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数学学科Seminar第2266讲 关于皮尔斯行列式:微分方程与渐近

创建时间:  2022/07/12  龚惠英   浏览次数:   返回

报告题目 (Title):On the Pearcey Determinant: Differential Equations and Asymptotics(关于皮尔斯行列式:微分方程与渐近)

报告人 (Speaker): 张仑 教授(复旦大学)

报告时间 (Time):2022年7月13日 (周三) 15:00

报告地点 (Place):腾讯会议(会议号:800-551-381)

邀请人(Inviter):何卓衡

主办部门:威尼斯娱乐官网地址下载(中国)有限公司数学系

报告摘要:

The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. In this talk, we are concerned with the Fredholm determinant $\det\left(I-\gamma K^{\mathrm{Pe}}_{s,\rho}\right)$, where $0 \leq \gamma \leq 1$ and $K^{\mathrm{Pe}}_{s,\rho}$ stands for the trace class operator acting on $L^2\left(-s, s\right)$ with the Pearcey kernel. We establish an integral representation of the Pearcey determinant involving the Hamiltonian associated with a family of special solutions to a system of nonlinear differential equations and obtain asymptotics of this determinant as $s\to +\infty$, which is also interpreted as large gap asymptotics in the context of random matrix theory. It comes out that the Pearcey determinant exhibits a significantly different asymptotic behavior for $\gamma=1$ and $0<\gamma<1$, which suggests a transition will occur as the parameter $\gamma$ varies. Based on joint works with Dan Dai and Shuai-Xia Xu.

上一条:物理学科Seminar第578讲 莫尔激子凝聚:非线性狄拉克点,破坏对称性的布洛赫波和非平庸的光选择定则

下一条:数学学科Seminar第2265讲 群的C*-代数及其K-理论简介


数学学科Seminar第2266讲 关于皮尔斯行列式:微分方程与渐近

创建时间:  2022/07/12  龚惠英   浏览次数:   返回

报告题目 (Title):On the Pearcey Determinant: Differential Equations and Asymptotics(关于皮尔斯行列式:微分方程与渐近)

报告人 (Speaker): 张仑 教授(复旦大学)

报告时间 (Time):2022年7月13日 (周三) 15:00

报告地点 (Place):腾讯会议(会议号:800-551-381)

邀请人(Inviter):何卓衡

主办部门:威尼斯娱乐官网地址下载(中国)有限公司数学系

报告摘要:

The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. In this talk, we are concerned with the Fredholm determinant $\det\left(I-\gamma K^{\mathrm{Pe}}_{s,\rho}\right)$, where $0 \leq \gamma \leq 1$ and $K^{\mathrm{Pe}}_{s,\rho}$ stands for the trace class operator acting on $L^2\left(-s, s\right)$ with the Pearcey kernel. We establish an integral representation of the Pearcey determinant involving the Hamiltonian associated with a family of special solutions to a system of nonlinear differential equations and obtain asymptotics of this determinant as $s\to +\infty$, which is also interpreted as large gap asymptotics in the context of random matrix theory. It comes out that the Pearcey determinant exhibits a significantly different asymptotic behavior for $\gamma=1$ and $0<\gamma<1$, which suggests a transition will occur as the parameter $\gamma$ varies. Based on joint works with Dan Dai and Shuai-Xia Xu.

上一条:物理学科Seminar第578讲 莫尔激子凝聚:非线性狄拉克点,破坏对称性的布洛赫波和非平庸的光选择定则

下一条:数学学科Seminar第2265讲 群的C*-代数及其K-理论简介

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