Concentration of Measure for Young Probabilists

Prerequisites: Familiarity with Probability: expected values, i.i.d sums. of independent variables, conditional expectation

1) Large deviations for i.i.d. sums (Crámer’s theorem).

2) Johnson-Lindenstrauss Lemma and extensions.

3) Concentration for functions of i.i.d. that are not sums; random graphs.

4) Empirical processes #1: how can one prove good bounds.

5) Empirical processes #2: VC families.