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.

该项目的目的是证明几种随机介质模型的（猜想）爱因斯坦关系。爱因斯坦的关系说，在有效运动的有效速度的0处的衍生物（作为偏见强度的函数）是由运动扩散而没有偏见的。更普遍地，我们希望研究随机过程作为输入参数的函数的有效参数，并且我们对单调性属性感兴趣。这种数量的例子是渗透簇上随机步行的有效扩散率，或者是定向渗透簇上的有效随机行走的有效扩散，作为渗透参数的功能。