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...
Enregistré dans:
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| Format: | Livre papier |
| Langue: | Anglais |
| Publié: |
Cham (Suisse) [etc.] :
Springer
C 2013.
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| Collection: | Lecture notes in mathematics. École d'été de probabilités de Saint-Flour
41 |
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| Note: |
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 |
| Résumé: | 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) |
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| Description: | 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 |
| Description matérielle: | 1 vol. (VII-129 p.) : ill. ; 24 cm. |
| Bibliographie: | Bibliogr. p. 125-129 |
| ISBN: | 9783319025759 (br.) 3319025759 (br.) |