Takashi Kumagai
eBook, PDF

Random Walks on Disordered Media and their Scaling Limits (eBook, PDF)

École d'Été de Probabilités de Saint-Flour XL - 2010

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In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster ('the ant in the labyrinth') is one o...

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