MARC details
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03336nam a22005175i 4500 |
| 001 - CONTROL NUMBER |
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978-3-319-02576-6 |
| 003 - CONTROL NUMBER IDENTIFIER |
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DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20150803155057.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
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131202s2013 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319025766 |
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978-3-319-02576-6 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-3-319-02576-6 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA440-699 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBM |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT012000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Benjamini, Itai. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Coarse Geometry and Randomness |
| Medium |
[electronic resource] : |
| Remainder of title |
École d’Été de Probabilités de Saint-Flour XLI – 2011 / |
| Statement of responsibility, etc |
by Itai Benjamini. |
| 264 #1 - |
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Cham : |
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Springer International Publishing : |
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Imprint: Springer, |
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2013. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
VII, 129 p. 6 illus., 3 illus. in color. |
| Other physical details |
online resource. |
| 336 ## - |
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text |
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txt |
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rdacontent |
| 337 ## - |
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computer |
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c |
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rdamedia |
| 338 ## - |
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online resource |
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cr |
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rdacarrier |
| 347 ## - |
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text file |
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PDF |
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rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Lecture Notes in Mathematics, |
| International Standard Serial Number |
0075-8434 ; |
| Volume number/sequential designation |
2100 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| 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. |
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| 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 |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical physics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Materials. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Graph Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematical Methods in Physics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Continuum Mechanics and Mechanics of Materials. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9783319025759 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Lecture Notes in Mathematics, |
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0075-8434 ; |
| Volume number/sequential designation |
2100 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-3-319-02576-6">http://dx.doi.org/10.1007/978-3-319-02576-6</a> |
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ZDB-2-SMA |
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ZDB-2-LNM |
