Titlebook: Selected Works of Oded Schramm; Itai Benjamini,Olle Häggström Book 2011 Springer Science+Business Media, LLC 2011 graph limits.history of

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Embeddings of Gromov Hyperbolic Spacesolic space. If one is allowed to rescale the metric of . by some positive constant, then there is an embedding where distances are distorted by at most an additive constant..Another embedding theorem states that any δ-hyperbolic metric space embeds isometrically into a complete geodesic δ-hyperbolic

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Noise Sensitivity of Boolean Functions and Applications to Percolationnfiguration with an arbitrary small percent of random errors gives almost no prediction whether the event occurs. On the other hand, weighted majority functions are shown to be noise-stable. Several necessary and sufficient conditions for noise sensitivity and stability are given..Consider, for exam

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Quantitative noise sensitivity and exceptional times for percolationn occurs. In doing so, new . noise sensitivity results for percolation are obtained. The latter is based on a novel method for controlling the “level .” Fourier coefficients via the construction of a randomized algorithm which looks at random bits, outputs the value of a particular function but look

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Recurrence of Distributional Limits of Finite Planar Graphstroduce the notion of a distributional limit . of such graphs. Assume that the vertex degrees of the vertices in .. are bounded, and the bound does not depend on .. Then after passing to a subsequence, the limit exists, and is a random rooted graph .. We prove that with probability one . is recurren

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Rigidity of Infinite (Circle) Packingsct as the circle packing theorem. The circle packing theorem also has a uniqueness part to it: if the graph is actually (the 1-skelaton of) a triangulation, then the circle packing is unique up to Möbius transformations.

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denauer Allee 24 53113 Bonn, Germany E-mail: sondermann@uni-bonn. de ISBN-10 3-540-34836-0 Springer Berlin Heidelberg New York ISBN-13 978-3-540-34836-8 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concer

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denauer Allee 24 53113 Bonn, Germany E-mail: sondermann@uni-bonn. de ISBN-10 3-540-34836-0 Springer Berlin Heidelberg New York ISBN-13 978-3-540-34836-8 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concer