000 | 03569nam a22005175i 4500 | ||
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001 | 978-3-319-03152-1 | ||
003 | DE-He213 | ||
005 | 20190213151435.0 | ||
007 | cr nn 008mamaa | ||
008 | 140124s2014 gw | s |||| 0|eng d | ||
020 |
_a9783319031521 _9978-3-319-03152-1 |
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024 | 7 |
_a10.1007/978-3-319-03152-1 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
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_aPBT _2bicssc |
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_aMAT029000 _2bisacsh |
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_aPBT _2thema |
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_aPBWL _2thema |
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_a519.2 _223 |
100 | 1 |
_aKumagai, Takashi. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aX, 147 p. 5 illus. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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_aÉcole d'Été de Probabilités de Saint-Flour, _x0721-5363 ; _v2101 |
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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 | _aDistribution (Probability theory. | |
650 | 0 | _aPotential theory (Mathematics). | |
650 | 1 | 4 |
_aProbability Theory and Stochastic Processes. _0http://scigraph.springernature.com/things/product-market-codes/M27004 |
650 | 2 | 4 |
_aMathematical Physics. _0http://scigraph.springernature.com/things/product-market-codes/M35000 |
650 | 2 | 4 |
_aPotential Theory. _0http://scigraph.springernature.com/things/product-market-codes/M12163 |
650 | 2 | 4 |
_aDiscrete Mathematics. _0http://scigraph.springernature.com/things/product-market-codes/M29000 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783319031514 |
776 | 0 | 8 |
_iPrinted edition: _z9783319031538 |
830 | 0 |
_aÉcole d'Été de Probabilités de Saint-Flour, _x0721-5363 ; _v2101 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-03152-1 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
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_c10679 _d10679 |