Coarse Geometry and Randomness: École d’Été de Probabilités de Saint-Flour XLI – 2011: Lecture Notes in Mathematics, cartea 2100
Autor Itai Benjaminien Limba Engleză Paperback – 19 dec 2013
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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Specificații
ISBN-13: 9783319025759
ISBN-10: 3319025759
Pagini: 140
Ilustrații: VII, 129 p. 6 illus., 3 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.2 kg
Ediția:2013
Editura: Springer International Publishing
Colecția Springer
Seriile Lecture Notes in Mathematics, École d'Été de Probabilités de Saint-Flour
Locul publicării:Cham, Switzerland
ISBN-10: 3319025759
Pagini: 140
Ilustrații: VII, 129 p. 6 illus., 3 illus. in color.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.2 kg
Ediția:2013
Editura: Springer International Publishing
Colecția Springer
Seriile Lecture Notes in Mathematics, École d'Été de Probabilités de Saint-Flour
Locul publicării:Cham, Switzerland
Public țintă
ResearchCuprins
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.
Textul de pe ultima copertă
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).
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).
Caracteristici
Includes many exercises of varying difficulty levels Investigates many open problems Presents topics not covered by any other book Includes supplementary material: sn.pub/extras