The Resource Coarse Geometry and Randomness : École d’Été de Probabilités de Saint-Flour XLI – 2011, by Itai Benjamini, (electronic resource)

Coarse Geometry and Randomness : École d’Été de Probabilités de Saint-Flour XLI – 2011, by Itai Benjamini, (electronic resource)

Label
Coarse Geometry and Randomness : École d’Été de Probabilités de Saint-Flour XLI – 2011
Title
Coarse Geometry and Randomness
Title remainder
École d’Été de Probabilités de Saint-Flour XLI – 2011
Statement of responsibility
by Itai Benjamini
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
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)
Member of
http://library.link/vocab/creatorName
Benjamini, Itai
Dewey number
516
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
mBdbGtTA6GY
Image bit depth
0
Language note
English
LC call number
QA440-699
Literary form
non fiction
Nature of contents
dictionaries
Series statement
École d'Été de Probabilités de Saint-Flour,
Series volume
2100
http://library.link/vocab/subjectName
  • Geometry
  • Distribution (Probability theory
  • Mathematical physics
  • Statistics
  • Mechanics
  • Mechanics, Applied
  • Geometry
  • Probability Theory and Stochastic Processes
  • Mathematical Methods in Physics
  • Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
  • Solid Mechanics
  • Graph Theory
Label
Coarse Geometry and Randomness : École d’Été de Probabilités de Saint-Flour XLI – 2011, by Itai Benjamini, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (VII, 129 p. 6 illus., 3 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783319025766
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-319-02576-6
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3710000000078755
  • (SSID)ssj0001090413
  • (PQKBManifestationID)11648211
  • (PQKBTitleCode)TC0001090413
  • (PQKBWorkID)11020662
  • (PQKB)10145321
  • (DE-He213)978-3-319-02576-6
  • (MiAaPQ)EBC3107018
  • (EXLCZ)993710000000078755
Label
Coarse Geometry and Randomness : École d’Été de Probabilités de Saint-Flour XLI – 2011, by Itai Benjamini, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (VII, 129 p. 6 illus., 3 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9783319025766
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-319-02576-6
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3710000000078755
  • (SSID)ssj0001090413
  • (PQKBManifestationID)11648211
  • (PQKBTitleCode)TC0001090413
  • (PQKBWorkID)11020662
  • (PQKB)10145321
  • (DE-He213)978-3-319-02576-6
  • (MiAaPQ)EBC3107018
  • (EXLCZ)993710000000078755

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