Concentration of Measure ∗

  title={Concentration of Measure ∗},
  author={Nathana{\"e}l Berestycki},
Often we want to show that some random quantity is close to its mean with high probability. Results of this kind are known as concentration inequalities. In this chapter we consider some important concentration results such as Hoeffding’s inequality, Bernstein’s inequality and McDiarmid’s inequality. Then we consider uniform bounds that guarantee that a set of random quantities are simultaneously close to their means with high probabilty. 

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