02791nam a2200373 i 4500991003263669707536160728t20142014sz a b 001 0 eng d9783319031514b14305434-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng519.223AMS 60G50AMS 05C81AMS 31C20AMS 35K08LC QA274.73Kumagai, Takashi525017Random walks on disordered media and their scaling limits :École d'Été de Probabilités de Saint-Flour XL - 2010 /Takashi KumagaiÉcole d'Été de Probabilités de Saint-Flour XL-2010Cham [Switzerland] :Springer,c2014x, 147 p. :ill. ;24 cmLecture notes in mathematics,0075-8434 ;2101Includes bibliographical references (pages 135-143) and indexIntroduction ; Weighted graphs and the associated Markov chains ; Heat kernel estimates general theory ; Heat kernel estimates using effective resistance ; Heat kernel estimates for random weighted graphs ; Alexander-Orbach conjecture holds when two-point functions behave nicely ; Further results for random walk on IIC ; Random conductance modelIn 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 notesRandom walksPotential theory (Mathematics)Distribution (Probability theory).b1430543425-11-1628-07-16991003263669707536LE013 60G KUM11 (2014)12013000293431le013pE36.39-l- 00000.i1578698511-11-16Random walks on disordered media and their scaling limits1392288UNISALENTOle01328-07-16ma -engsz 00