Home » Random Walks on Disordered Media and Their Scaling Limits: Ecole DEte de Probabilites de Saint-Flour XL - 2010 by Takashi Kumagai
Random Walks on Disordered Media and Their Scaling Limits: Ecole DEte de Probabilites de Saint-Flour XL - 2010 Takashi Kumagai

Random Walks on Disordered Media and Their Scaling Limits: Ecole DEte de Probabilites de Saint-Flour XL - 2010

Takashi Kumagai

Published February 4th 2014
ISBN : 9783319031514
Paperback
147 pages
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 About the Book 

In these lecture notes, we will analyze the behavior of random walk on disordered mediaby means ofboth probabilistic and analytic methods, and will study the scalinglimits. We will focus on the discrete potential theory and how the theory isMoreIn these lecture notes, we will analyze the behavior of random walk on disordered mediaby means ofboth probabilistic and analytic methods, and will study the scalinglimits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media.Thefirst few chapters of the notes can be used as an introduction to discrete potential theory.Recently, there has beensignificantprogress on thetheoryof random walkon disordered media such as fractals and random media.Random walk on a percolation cluster( the ant in the labyrinth )is one of the typical examples. In 1986, H. Kesten showedtheanomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.