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.

我们已经建立了通用结构定理和一个SDE代表定理，用于与2D库仑电势相互作用。我们已经将它们应用于由随机基质理论（例如Ginibre，Dyson，Bessel随机点场）引起的代表性随机点字段，并检测并求解并求解了描述相关随机动力学的无限二二维随机微分方程。我们证明，Ginibre随机点场的手掌测量具有非常奇怪的特性，这与Ruelle的类相互作用电位的通常的Gibbs度量截然不同。我们已经构建了2D Young图的时间进化模型，并证明了其缩放限制。

项目成果

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

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

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

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

Interfaces in a stochastic reaction-diffusion equation and an evolutional model of Young diagrams

随机反应扩散方程中的界面和杨图的演化模型

• 发表时间: 2011
• 作者: Nakayama;Y.;Kikuta;H.;Kanai;M.;Yoshikawa;K.;Kawamura;A.;Kobayashi;K.;Wang;Z.;Khan;A.;Kawakami;K.;and Yamasu;K.;Ken'ichi Ohshika;S. Takayama;舟木直久
• 通讯作者: 舟木直久