stochastic growth models in random environments and their phase transition

随机环境中的随机增长模型及其相变

• 批准号: 21540125
• 负责人: YOSHIDA Nobuo
• 金额: $ 2.58万
• 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: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540125/
• 关键词: ランダム環境; 相転移; 確率成長; ランダム媒質

We consider a discrete-time stochastic growth model on d-dimensional lattice.The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the ``total number of particles" in this framework.The main results are roughly as follows: If d ≧ 3 and the system is ``not too random", then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is ``random enough", then the growth rate is slower than its expectation.

我们考虑 d 维晶格上的离散时间随机增长模型。增长模型描述了各种有趣的例子，例如定向位点/键渗流、随机环境中的定向聚合物、二元接触路径过程的时间离散和我们研究的选民模型。该框架中“粒子总数”增长率的相变。主要结果大致如下： 如果 d ≥ 3 并且系统“不太随机”，那么，正概率，粒子总数的增长率与其期望的增长率相同，另一方面，如果 d=1,2，或者系统“足够随机”，那么增长率会比预期慢。它的期望。

项目成果

Stochastic Power Law Fluids : Existence and Uniqueness of Weak Solutions

随机幂律流体:弱解的存在性和唯一性

• 发表时间: 2011
• 作者: Yutaka Terasawa; Nobuo Yoshida
• 通讯作者: Nobuo Yoshida

Brownian Directed Polymers in Random Environment: Complete Localization and Phase Diagram.

随机环境中的布朗定向聚合物：完整的定位和相图。

• 发表时间: 2013
• 作者: Nobuo Yoshida

Linear Stochastic Growth Models

线性随机增长模型

• 发表时间: 2011
• 作者: Nobuo Yoshida

Stochastic Power Law Fluids

随机幂律流体

• 发表时间: 2011
• 作者: Nobuo Yoshida

Stochastic Shear Thickening Fluids: Strong Convergence of the Garelkin Approximation and the Energy Equality

随机剪切稠化流体：Garelkin 近似与能量等式的强收敛性

• 发表时间: 2011
• 作者: Nobuo Yoshida