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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
020 _a9783319025766
_9978-3-319-02576-6
024 7 _a10.1007/978-3-319-02576-6
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aBenjamini, Itai.
_eauthor.
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.
300 _aVII, 129 p. 6 illus., 3 illus. in color.
_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 ;
_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 _aMathematics.
650 0 _aGeometry.
650 0 _aMathematical physics.
650 0 _aMaterials.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aGraph Theory.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
650 2 4 _aContinuum Mechanics and Mechanics of Materials.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319025759
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2100
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02576-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c6950
_d6950