Coarse Geometry and Randomness ©0cole dỚ"©0t©♭ de Probabilit©♭s de Saint-Flour XLI Ớ<U+001c> 2011 /

• Main Author: Benjamini, Itai. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2100
• Subjects: Mathematics.; Geometry.; Probabilities.; Graph theory.; Physics.; Statistics.; Continuum mechanics.; Probability Theory and Stochastic Processes.; Mathematical Methods in Physics.; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.; Continuum Mechanics and Mechanics of Materials.; Graph Theory.
• Online Access: View fulltext via EzAccess

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. T...

Table of 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.