Introduction to graph theory
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Cayley graphs: eigenvalues, expanders and random walks
Surveys in combinatorics, 1995
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We present the anisotropic version of the classical Alon-Boppana theorem on the asymptotic spectrum of random walks on infinite families of graphs. The relations to the Grigorchuk-Zuk theory--on the space of graphs with uniformly bounded degree and the continuity of the spectral measure of Markov operators related to the Alon-Boppana theorem and the Burger-Greenberg-Serre theorem--are also indicated.