Coarse geometry and randomness
These 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. T...
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| Hlavní autor: | |
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| Korporativní autor: | |
| Médium: | Livre papier |
| Jazyk: | Anglais |
| Vydáno: |
Cham (Suisse) [etc.] :
Springer
C 2013.
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| Edice: | Lecture notes in mathematics. École d'été de probabilités de Saint-Flour
41 |
| Témata: | |
| Poznámka: |
Cours donnés durant la 41ème Ecole d'été de probabilités de Saint-Flour (Cantal) en 2011 ISSN et numérotation de la collection principale : 0075-8434 ; 2100 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Coarse geometry and randomness, École d Été de Probabilités de Saint-Flour XLI 2011, 1st ed. 2013., 20XX, Cham, Springer International Publishing, Lecture notes in mathematics, 978-3-319-02576-6 |
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| 110 | 2 | |a École d'été de probabilités de Saint-Flour |n (41 |d :2011 |c :Saint-Flour, Cantal). |4 aut | |
| 245 | 1 | 0 | |a Coarse geometry and randomness |c École d'Été de Probabilités de Saint-Flour XLI - 2011 ; Itai Benjamini. |
| 260 | |a Cham (Suisse) [etc.] : |b Springer. | ||
| 260 | |c C 2013. | ||
| 300 | |a 1 vol. (VII-129 p.) : |b ill. ; |c 24 cm. | ||
| 490 | 0 | |a Lecture notes in mathematics. École d'été de probabilités de Saint-Flour |v 41 | |
| 500 | |a Cours donnés durant la 41ème Ecole d'été de probabilités de Saint-Flour (Cantal) en 2011 | ||
| 500 | |a ISSN et numérotation de la collection principale : 0075-8434 ; 2100 | ||
| 504 | |a Bibliogr. p. 125-129 | ||
| 505 | 0 | |a Isoperimetry 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 | |a These 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 | |a Géométrie | ||
| 650 | |a Processus stochastiques | ||
| 650 | |a Percolation (physique statistique) | ||
| 650 | |a Marches aléatoires (mathématiques) | ||
| 650 | |a Géométrie combinatoire | ||
| 650 | |a Théorie des graphes | ||
| 650 | |a Actes de congrès | ||
| 700 | 1 | |a Benjamini, Itai, |d 19..- |4 aut | |
| 776 | 0 | |0 176106332 |t Coarse geometry and randomness |f École d Été de Probabilités de Saint-Flour XLI 2011 |e 1st ed. 2013. |d 20XX |c Cham |n Springer International Publishing |s Lecture notes in mathematics |z 978-3-319-02576-6 | |
| 997 | |0 517899 |1 Livre papier |a Ressource papier |c 0/Orléans/ |c 1/Orléans/IDP/ |z Orléans, IDP, LNM 2100 | ||