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020   $a9783319031514
035   $ab14305434-39ule_inst
040   $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 04$a519.2$223
084   $aAMS 60G50
084   $aAMS 05C81
084   $aAMS 31C20
084   $aAMS 35K08
084   $aLC QA274.73
100 1 $aKumagai, Takashi$0525017
245 10$aRandom walks on disordered media and their scaling limits :$bÉcole d'Été de Probabilités de Saint-Flour XL - 2010 /$cTakashi Kumagai
246 30$aÉcole d'Été de Probabilités de Saint-Flour XL-2010
260   $aCham [Switzerland] :$bSpringer,$cc2014
300   $ax, 147 p. :$bill. ;$c24 cm
440  0$aLecture notes in mathematics,$x0075-8434 ;$v2101
504   $aIncludes bibliographical references (pages 135-143) and index
505 0 $aIntroduction ; 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 model
520   $aIn these lecture notes, we will analyze the behavior of random walk on disordered mediaby means ofboth probabilistic and analytic methods, and will study the scalinglimits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media.Thefirst few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has beensignificantprogress on thetheoryof random walkon disordered media such as fractals and random media.Random walk on a percolation cluster('the ant in the labyrinth')is one of the typical examples. In 1986, H. Kesten showedtheanomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes
650  0$aRandom walks
650  0$aPotential theory (Mathematics)
650  0$aDistribution (Probability theory)
907   $a.b14305434$b25-11-16$c28-07-16
912   $a991003263669707536
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996   $aRandom walks on disordered media and their scaling limits$91392288
997   $aUNISALENTO
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