Concentration of measure for the analysis of randomized algorithms by Devdatt P. Dubhashi and Alessandro Panconesi Cambridge University Press, 2009

The utility of probabilistic methods in the computational context is one of the fundamental discoveries of computer science over the last four decades. In the analysis (and design) of randomized algorithms or stochastic processes, the tool required by far is one showing that certain types of random variables remain “close enough” to their means – or medians, in a few cases – with high probability. In fact, many randomized algorithms can be designed using the following recipe: “assume that the relevant random variables stay close enough to their means, and prove that everything works out”. The trick, of course, is to be able to prove such “concentration of measure” results. While the Chernoff bounds are perhaps well-known to theoretical computer scientists, their independence assumptions often do not hold, and we need more sophisticated machinery to handle all manner of correlations. This book brings together essentially all of the relevant state-of-the-art in a manner that is particularly appealing to computer scientists and to those with discrete sensibilities. A disclaimer: I have co-authored papers with both of the authors, but believe this review to be unbiased.