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035   $a(DE-He213)978-3-319-02576-6
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100   $a20131202d2013      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aCoarse Geometry and Randomness $eÉcole d?Été de Probabilités de Saint-Flour XLI ? 2011 /$fby Itai Benjamini
205   $a1st ed. 2013.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2013.
215   $a1 online resource (VII, 129 p. 6 illus., 3 illus. in color.) 
225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2100
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-02575-9 
327   $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.
330   $aThese lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ).
410  0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2100
606   $aGeometry
606   $aProbabilities
606   $aPhysics
606   $aStatistics 
606   $aMechanics
606   $aMechanics, Applied
606   $aGraph theory
606   $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020
606   $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010
606   $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020
615  0$aGeometry.
615  0$aProbabilities.
615  0$aPhysics.
615  0$aStatistics .
615  0$aMechanics.
615  0$aMechanics, Applied.
615  0$aGraph theory.
615 14$aGeometry.
615 24$aProbability Theory and Stochastic Processes.
615 24$aMathematical Methods in Physics.
615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
615 24$aSolid Mechanics.
615 24$aGraph Theory.
676   $a519.2
700   $aBenjamini$b Itai$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479680
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910438159403321
996   $aCoarse geometry and randomness$9258662
997   $aUNINA