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Concentration of Measure for the Analysis of Randomized Algorithms by Alessandro Panconesi, Devdatt P. Dubhashi

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10

Isoperimetric Inequalities and Concentration

In this chapter we introduce the notion of isoperimetric inequalities. These inequalities constitute another important approach to proving concentration inequalities. We start by explaining what an isoperimetric inequality means in an abstract form and then give a few classical examples. We explain how isoperimetric inequalities easily yield concentration inequalities. Finally we concentrate on an important isoperimetric inequality in discrete product spaces with a Hamming distance, showing how, in many situations, it is essentially equivalent to the method of bounded differences.

This chapter lays the groundwork for Chapters 12 and 13, where methods are developed to prove such isoperimetric inequalities ...

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