Research on Spectra of Random Schrodinger Operators

随机薛定谔算子谱的研究

• 批准号: 18540171
• 负责人: UEKI Naomasa
• 金额: $ 2.43万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540171/
• 关键词: Stochastic Analysis; Differential Equations; Operator Theory; Mathematical Physics; Random Schrodinger Operators; Random Matrix; Spectrum; Schrodinger Operators; Stochastic Analysis; Differential Equations; Operator Theory; Mathematical Physics; Random Schrodinger Operators; Random Matrix; Spectrum; Schrodinger Operators

The aim of this project is to held international workshops to promote the research on random operators in Japan. The main workshop was held for 5 days from 2006 December 11 (Monday) to 15 (Friday) at Kyoto University, Yoshida South Campus. The title was "Spectral Theory of Random Operators and Related Fields in Probability Theory", the amount of the participants were about 50 including 7 guests invited from abroad, and we could have meaningful occasions for exchanging ideas for researches. Another smaller workshop was held for 3 days from 2007 November 14 (Wednesday) to 16 (Friday) at Kyoto University, Graduate School of Human and Environmental Studies. The title was "Spectra of Random Operators and Related Fields", the amount of the participants was about 30 including 1 guest from abroad and we could have close communications on researches. The topics treated in these workshops were very substantial. Those were mainly on random Schrodinger operators and random matrices. Moreover various topics on financial and political sciences were also treated. The topics on random operators were mainly from mathematical viewpoints. Moreover the topics from physical viewpoints were also treated. In these workshops, Ueki gave a lecture on a refinement of Hislop-Klopp theory on the Wegner estimate for Schrodinger operators with random vector potentials and its applications to the proof of the Anderson localization. Minami gave lectures on a conjecture on energy level statistics for the Anderson model. Nakamura gave a lecture on the results on the semi-classical characterization of the wave front set of Schrodinger equations. Kotani gave a lecture on the construction of the KdV flow having stationarity with respect to the space-time variables by Sato's theory on the dynamical system on the infinite dimensional Grassmanian manifolds.

该项目的目的是举办国际研讨会，以促进对日本随机运营商的研究。主要研讨会从2006年12月11日（星期一）到15（星期五）在吉田南校园的京都大学举行了5天。标题是“概率理论中随机运算符和相关领域的光谱理论”，参与者的数量约为50个，其中包括来自国外的7名客人，我们可以有有意义的机会来交换研究思想的研究。从2007年11月14日（星期三）到京都大学，人类和环境研究研究生院，另一个较小的研讨会在京都大学举行了3天。标题是“随机运营商和相关领域的光谱”，参与者的数量约为30个，其中包括来自国外的1位客人，我们可以在研究方面进行密切的沟通。这些研讨会中处理的主题非常重要。这些主要是在随机的Schrodinger操作员和随机矩阵上。此外，还介绍了有关财务和政治科学的各种主题。随机运算符的主题主要来自数学观点。此外，还处理了物理观点的主题。在这些研讨会中，Ueki就HISLOP-KLOPP理论进行了关于Wegner估算的简化介绍，该理论对具有随机向量潜力的Schrodinger操作员及其在Anderson本地化证明中的应用。 Minami就Anderson模型的能量水平统计数据进行了讲座。 Nakamura就Schrodinger方程的波前集的半古典表征进行了演讲。 Kotani就Sato在无限尺寸格拉马尼亚歧管上的动力学系统上的理论进行了关于时空变量具有平稳性的KDV流的构建的讲座。