Coarse Geometry and Randomness (Record no. 29308)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03425nam a22005295i 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783319025766 |
| -- | 978-3-319-02576-6 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516 |
| 100 1# - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Benjamini, Itai. |
| 245 10 - TITLE STATEMENT | |
| Title | Coarse Geometry and Randomness |
| Sub Title | École d’Été de Probabilités de Saint-Flour XLI – 2011 / |
| Statement of responsibility, etc | by Itai Benjamini. |
| 260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Cham : |
| Name of publisher | Springer International Publishing : |
| -- | Imprint: Springer, |
| Year of publication | 2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | VII, 129 p. 6 illus., 3 illus. in color. |
| Other physical details | online resource. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Lecture Notes in Mathematics, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 ## - SUMMARY, ETC. | |
| Summary, etc | 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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematical physics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Materials. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Graph Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematical Methods in Physics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Continuum Mechanics and Mechanics of Materials. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-319-02576-6 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E-BOOKS |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2013. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 0075-8434 ; |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|
| IMSc Library | EBK14 | http://dx.doi.org/10.1007/978-3-319-02576-6 | E-BOOKS |