Eyal Rozenman

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We introduce a “derandomized” analogue of graph squaring. This operation increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree. One application of this product is an alternative proof of(More)
We construct a sequence of groups Gn, and explicit sets of generators Yn ⊂ Gn, such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 is the alternating group Ad, the set of even permutations on the elements {1, 2, . . . , d}. The group Gn is the group of all even symmetries of the rooted d-regular(More)
Let G 1⁄4 ðIn;EÞ be the graph of the n-dimensional cube. Namely, In 1⁄4 f0; 1g and 1⁄2x; y 2 E whenever jjx yjj1 1⁄4 1. For A In and x 2 A define hAðxÞ 1⁄4 #fy 2 In n Aj1⁄2x; y 2 Eg, i.e., the number of vertices adjacent to x outside of A. Talagrand, followingMargulis, proves that for every set A In of size 2n 1 we have 1 2n P x2A(More)
This is a survey of pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number(More)
Pseudorandomness is the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This survey of the subject places particular emphasis on the intimate connections that have been discovered between a variety of fundamental “pseudorandom objects” that at first seem very different in nature: expander(More)
This is the second volume of a 2-part survey on pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. The survey places particular emphasis on the intimate connections that have been discovered between a variety of fundamental “pseudorandom objects” that at first seem very(More)