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101 0 $aeng
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200 10$aRandom Walks on Disordered Media and their Scaling Limits$b[electronic resource] $eÉcole d'Été de Probabilités de Saint-Flour XL - 2010 /$fby Takashi Kumagai
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (X, 147 p. 5 illus.) 
225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2101
300   $aThese are notes from a series of eight lectures given at the Saint-Flour Probability Summer School, July 4-17, 2010 -- Page vii.
311   $a3-319-03151-1 
320   $aIncludes bibliographical references (pages 135-143) and index.
327   $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.
330   $aIn these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory.   Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster (?the ant in the labyrinth?) is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.
410  0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2101
606   $aProbabilities
606   $aMathematical physics
606   $aPotential theory (Mathematics)
606   $aDiscrete mathematics
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163
606   $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000
608   $aCongressen (vorm)$2gtt
615  0$aProbabilities.
615  0$aMathematical physics.
615  0$aPotential theory (Mathematics).
615  0$aDiscrete mathematics.
615 14$aProbability Theory and Stochastic Processes.
615 24$aMathematical Physics.
615 24$aPotential Theory.
615 24$aDiscrete Mathematics.
676   $a519.282
700   $aKumagai$b Takashi$4aut$4http://id.loc.gov/vocabulary/relators/aut$0525017
712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(40th :$f2010)
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996205189203316
996   $aRandom walks on disordered media and their scaling limits$91392288
997   $aUNISA