Einstein-Relation und das Verhalten effektiver Parameter im zufälligen Medium

爱因斯坦关系和随机介质中有效参数的行为

• 批准号: 229644794
• 负责人: Professorin Dr. Nina Jael Gantert
• 金额: --
• 依托单位: Lehrstuhl für Wahrscheinlichkeitstheorie (M14)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/229644794?language=en
• 关键词: Einstein; Relation; und; das; Verhalten

The goal of the project is to prove the (conjectured) Einstein relation for several random media models.The Einstein relation says that the derivative at 0 of the effective velocity of a biased motion (as a function of the strength of the bias) is given by the diffusivity of the motion without bias. More generally, we want to investigate the effective parameters of a stochastic process as functions of the input parameters, and we are interested in monotonicity properties. Examples of such quantities are the effective diffusivity of random walks on percolation clusters or the effective diffusivity of directed random walks on oriented percolation clusters, as functions of the percolation parameter.

该项目的目标是证明几种随机介质模型的爱因斯坦关系。爱因斯坦关系表示有偏运动的有效速度在0处的导数（作为偏置强度的函数）由无偏运动的扩散率给出。更一般地说，我们希望研究随机过程的有效参数作为输入参数的函数，我们感兴趣的是单调性。这样的数量的例子是有效的扩散率的随机游动的渗流集群或有效的扩散率定向随机游动定向渗流集群，作为函数的渗流参数。