By Itai Benjamini
These lecture notes examine the interaction among randomness and geometry of graphs. the 1st a part of the notes reports numerous simple geometric techniques, prior to relocating directly to research the manifestation of the underlying geometry within the habit of random approaches, in most cases percolation and random walk.
The learn of the geometry of countless vertex transitive graphs, and of Cayley graphs particularly, within reason good built. One aim of those notes is to indicate to a couple random metric areas modeled through graphs that turn into just a little unique, that's, they admit a mix of homes now not encountered within the vertex transitive global. those contain percolation clusters on vertex transitive graphs, serious clusters, neighborhood and scaling limits of graphs, lengthy diversity percolation, CCCP graphs received via contracting percolation clusters on graphs, and desk bound random graphs, together with the uniform endless planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ).
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Extra resources for Coarse Geometry and Randomness: École d’Été de Probabilités de Saint-Flour XLI – 2011 (Lecture Notes in Mathematics)
Coarse Geometry and Randomness: École d’Été de Probabilités de Saint-Flour XLI – 2011 (Lecture Notes in Mathematics) by Itai Benjamini