RANDOM GRAPHS (Wiley Interscience Series in Discrete Mathematics and Optimization)

By William T. Gowers. 2001

580 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4d927cbbe27bbcfab4d5d49674c7cca354962b13

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In Artificial Intelligence

In Computational Theory and Mathematics

Citations in the corpus

Random Graphs and Complex Networks (2016, methodology): “These other models are also partly covered in the classical works Boll01 [40] and JanLucRuc00 [124], but up to today, there is no text treating random graphs and random graph models for complex networks in a relatively elementary way.”
Percolation on finite graphs and isoperimetric inequalities (2002, methodology): “The techniques we use can also be used to give a significantly shorter proof than those previously known for the fact that the critical probability for percolation onZd is asymptotically 1/(2d) asd → ∞.”
Random walks on the random graph (2015, background): “It is well-known (see [5,10,16,27]) that D̄, the average distance between two vertices in C1, is logλ n + Op(1), analogous to the fact that D̄ = logd−1 n + Op(1) in G(n, d), the uniform d-regular graph on n vertices (both are locally-tree-like: G(n, d) resembles a d-regular tree while G(n, p) resemb”
Fundamentals of Stein's method (2011, background): “These objects are a simple and classical model of networks that are well studied; see [14, 37] for book length treatments.”
Novel scaling limits for critical inhomogeneous random graphs (2009, unknown): “, the monographs [2, 5, 10, 19, 29] and the references therein).”
Large deviations of empirical neighborhood distribution in sparse random graphs (2013, methodology): “To this end we introduce a natural extension of the usual configuration model from [8], see also [25].”
Applications of Stein's method for concentration inequalities (2009, background): “The behavior of the upper tail of subgraph counts in G(n, p) is a problem of great interest in the theory of random graphs (see [6, 25, 27, 28, 39], and references contained therein).”