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Kowalski E. An introduction to expander graphs

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Kowalski E. An introduction to expander graphs
Zurich: ETH, 2018. — 233 p.
Contents :
Preface
Chapter Introduction and motivation
Prerequisites and notation
Graphs
Metric, diameter, and so on
Cayley graphs, action graphs, Schreier graphs
Expansion in graphs
Random walks
Random walks and expansion
The discrete Laplace operator
Expansion of Cayley graphs
Matchings
Probabilistic existence of expanders
Ramanujan graphs
Cayley graphs of finite linear groups
Property (T)
The Barzdin-Kolmogorov graph-embedding theorem
Error reduction in probabilistic algorithms
Sieve methods
Geometric applications
Diophantine applications
Preliminaries and strategy
The Bourgain-Gamburd argument
Implementing the Bourgain-Gamburd argument
Quasi-random groups
Growth of generating subsets of `39`42`"613A``45`47`"603ASL2(Fp)
Proof of the growth theorem
Introduction
Diagrams
Statements and proofs
Free groups
Properties of `39`42`"613A``45`47`"603ASL2
Finite-dimensional unitary representations of abelian groups
Algebraic integers
Real stable polynomials
Mixed characteristic polynomials
Bibliography
Index of notation
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