000 | 04007nam a22005655i 4500 | ||
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001 | 978-3-319-02576-6 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 131202s2013 gw | s |||| 0|eng d | ||
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_a9783319025766 _9978-3-319-02576-6 |
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_a10.1007/978-3-319-02576-6 _2doi |
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_aPBM _2bicssc |
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_aMAT012000 _2bisacsh |
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_aPBM _2thema |
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_a516 _223 |
100 | 1 |
_aBenjamini, Itai. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aCoarse Geometry and Randomness _h[electronic resource] : _bÉcole d’Été de Probabilités de Saint-Flour XLI – 2011 / _cby Itai Benjamini. |
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2013. |
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300 |
_aVII, 129 p. 6 illus., 3 illus. in color. _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 ; _v2100 |
|
505 | 0 | _aIsoperimetry and expansions in graphs -- Several metric notions -- The hyperbolic plane and hyperbolic graphs -- More on the structure of vertex transitive graphs -- Percolation on graphs -- Local limits of graphs -- Random planar geometry -- Growth and isoperimetric profile of planar graphs -- Critical percolation on non-amenable groups -- Uniqueness of the infinite percolation cluster -- Percolation perturbations -- Percolation on expanders -- Harmonic functions on graphs -- Nonamenable Liouville graphs. | |
520 | _aThese lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ). | ||
650 | 0 | _aGeometry. | |
650 | 0 | _aDistribution (Probability theory. | |
650 | 0 | _aMathematical physics. | |
650 | 0 | _aStatistics. | |
650 | 0 | _aMechanics. | |
650 | 0 | _aMechanics, Applied. | |
650 | 1 | 4 |
_aGeometry. _0http://scigraph.springernature.com/things/product-market-codes/M21006 |
650 | 2 | 4 |
_aProbability Theory and Stochastic Processes. _0http://scigraph.springernature.com/things/product-market-codes/M27004 |
650 | 2 | 4 |
_aMathematical Methods in Physics. _0http://scigraph.springernature.com/things/product-market-codes/P19013 |
650 | 2 | 4 |
_aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. _0http://scigraph.springernature.com/things/product-market-codes/S17020 |
650 | 2 | 4 |
_aSolid Mechanics. _0http://scigraph.springernature.com/things/product-market-codes/T15010 |
650 | 2 | 4 |
_aGraph Theory. _0http://scigraph.springernature.com/things/product-market-codes/M29020 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783319025759 |
776 | 0 | 8 |
_iPrinted edition: _z9783319025773 |
830 | 0 |
_aÉcole d'Été de Probabilités de Saint-Flour, _x0721-5363 ; _v2100 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-02576-6 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c10392 _d10392 |