What is . . . An expander

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From Apollonius To Zaremba: Local-Global Phenomena in Thin Orbits (2012, background): “r arcs M.) To explain how this happens, we brie y discuss the notion of an expander. Rather than going into the general theory (for which we refer the reader to the beautiful survey [Lub12]; see also [Sar04]), we content ourselves with but one illustrative example of expansion. Figure13 shows the fo”
Uniform expansion bounds for Cayley graphs of SL2(Fp) (2008, background): “Expanders are highly-connected sparse graphs widely used in computer science, in areas ranging from parallel computation to complexity theory and cryptography; recently they also have found some remarkable applications in pure mathematics; see [5],[10], [15], [20], [21] and references therein.”
Poisson–Dirichlet distribution for random Belyi surfaces (2005, background): “(3.1) A family of k-regular graphs Xn,k forms a family of C-expanders [34, 46] if there is a fixed positive constant C such that lim inf n→∞ c(Xn,k) ≥ C.(3.2) The adjacency matrix of G, A(G), is the |G| by |G| matrix, with rows and columns indexed by vertices of G, such that the x, y entry is 1 if a”
Affine linear sieve, expanders, and sum-product (2010, background): “See Section 4 and [32, 50] for definitions and properties of expanders.”