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001  9783319031521  
003  DEHe213  
005  20150803155057.0  
007  cr nn 008mamaa  
008  140124s2014 gw  s  0eng d  
020 
_a9783319031521 _99783319031521 

024  7 
_a10.1007/9783319031521 _2doi 

050  4  _aQA273.A1274.9  
050  4  _aQA274274.9  
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 SaintFlour 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, _x00758434 ; _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  AlexanderOrbach conjecture holds when twopoint 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, _x00758434 ; _v2101 

856  4  0  _uhttp://dx.doi.org/10.1007/9783319031521 
912  _aZDB2SMA  
912  _aZDB2LNM  
950  _aMathematics and Statistics (Springer11649)  
999 
_c6955 _d6955 