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001 978-3-319-03152-1
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008 140124s2014 gw | s |||| 0|eng d
020 _a9783319031521
_9978-3-319-03152-1
024 7 _a10.1007/978-3-319-03152-1
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aKumagai, Takashi.
_eauthor.
245 1 0 _aRandom Walks on Disordered Media and their Scaling Limits
_h[electronic resource] :
_bÉcole d'Été de Probabilités de Saint-Flour XL - 2010 /
_cby Takashi Kumagai.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aX, 147 p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2101
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 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
650 0 _aMathematics.
650 0 _aPotential theory (Mathematics).
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aMathematical Physics.
650 2 4 _aPotential Theory.
650 2 4 _aDiscrete Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319031514
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2101
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-03152-1
912 _aZDB-2-SMA
912 _aZDB-2-LNM
950 _aMathematics and Statistics (Springer-11649)
999 _c6955
_d6955