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个随机介质模型的（推测的）爱因斯坦关系。爱因斯坦关系表示，偏置运动的有效速度在 0 处的导数（作为偏置强度的函数）给出通过无偏差运动的扩散率。更一般地说，我们想要研究随机过程的有效参数作为输入参数的函数，并且我们对单调性感兴趣。此类量的示例是渗流簇上随机游走的有效扩散率或定向渗流簇上定向随机游走的有效扩散率，作为渗流参数的函数。