Infinite-dimensional stochastic dynamical systems motivated by random matrices and statistical physics

由随机矩阵和统计物理驱动的无限维随机动力系统

• 批准号: 21340031
• 负责人: OSADA Hirofumi
• 金额: $ 10.65万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21340031/
• 关键词: 確率解析; 対数ガス; クーロンポテンシャル; 無限次元確率力学系; ランダム行列; 干渉ブラウン運動; 点過程; 拡散過程; 統計物理; logガス; random point fields; random Point fields

We have established a general construction theorem and an SDE representation theorem for interacting Brownian motions with 2D Coulomb potentials. We have applied them to the representative random point fields arising from Random Matrix Theory such as Ginibre, Dyson, Bessel random point fields, and have detected and solve the infinite-dimensional stochastic differential equations describing the associated stochastic dynamics. We prove the Palm measures of Ginibre random point field have very strange property that is very different from usual Gibbs measures with Ruelle' s class interaction potentials. We have constructed the time evolutional model of 2D Young diagram and have proved its scaling limit.

我们建立了具有二维库仑势的相互作用布朗运动的一般构造定理和表示定理。我们将它们应用于随机矩阵理论中的代表性随机点场，如Ginibre，Dyson，Bessel随机点场，并检测和求解了描述相关随机动力学的无穷维随机微分方程。证明了Ginibre随机点场的Palm测度具有与通常的具有Ruelle类相互作用势的Gibbs测度不同的奇异性质。我们建立了二维杨氏图的时间演化模型，并证明了它的标度极限。

项目成果

Noncolliding processes, Matrix-valued process and determinatal processes

非碰撞过程、矩阵值过程和确定性过程

• 发表时间: 2011
• 期刊: SUGAKU EXPOSITIONS
• 作者: H. Osada;H. Tanemura;Makoto Katori and Hideki Tanemura;Makoto Katori;Makoto Katori
• 通讯作者: Makoto Katori

Infinite Particle Systems associated with Airy kernel

与 Airy 内核相关的无限粒子系统

• 发表时间: 2011
• 作者: H. Osada;H. Tanemura;Makoto Katori and Hideki Tanemura;Makoto Katori;Makoto Katori;Makoto Katori and Hideki Tanemura;種村 秀紀;種村 秀紀;Hideki Tanemura;種村秀紀;種村秀紀;Hideki Tanemura;Hideki Tanemura;Hideki Tanemura;Hideki Tanemura;Hideki Tanemura
• 通讯作者: Hideki Tanemura

Hydrodynamic limit for the $￥vnabla￥arphi$ interface model via two-scale approach

通过两尺度方法的 $vnablaarphi$ 界面模型的流体动力学极限

• 发表时间: 2012
• 期刊: In : Probability in Complex Physical Systems, the Festschrift for Bolthausen and G￥"artner
• 作者: Raiji Mukae;Atsuhiro Nakamoto;磯崎洋;Tadahisa Funaki
• 通讯作者: Tadahisa Funaki

Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials

• DOI: 10.1214/11-aop736
• 发表时间: 2009-02
• 期刊: Annals of Probability
• 影响因子: 2.3
• 作者: H. Osada

Non-equilibrium dynamics of Dyson's model with an infinite number of particles

具有无限数量粒子的戴森模型的非平衡动力学

• 发表时间: 2010
• 期刊: Commun.Math.Phys. 293
• 作者: Makoto Katori;Hideki Tanemura
• 通讯作者: Hideki Tanemura