Combinatorica
Eigenvalues, Expanders And Superconcentrators
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Strong converse for identification via quantum channels
IEEE Transactions on Information Theory
Random Structures & Algorithms
Ranking and sparsifying a connection graph
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
Loose laplacian spectra of random hypergraphs
Random Structures & Algorithms
The chromatic number of random Cayley graphs
European Journal of Combinatorics
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The AlonRoichman theorem states that for every ε 0there is a constant c(ε), such that the Cayley graphof a finite group G with respect to c(ε)log|G| elements of G, chosen independently and uniformlyat random, has expected second largest eigenvalue less thanε. In particular, such a graph is an expander with highprobability.Landau and Russell, and independently Loh and Schulman, improvedthe bounds of the theorem. Following Landau and Russell we give anew proof of the result, improving the bounds even further. Whenconsidered for a general group G, our bounds are in a sensebest possible. We also give a generalization of the AlonRoichmantheorem to random coset graphs.Our proof uses a Hoeffding-type result for operator valuedrandom variables, which we believe can be of independent interest.© 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008