Talagrand’s Inequality in Hereditary Settings

We develop a nicely packaged form of Talagrand's inequality that<br />can be applied to prove concentration of measure for functions defined by hereditary properties. We illustrate the framework with several applications from combinatorics and algorithms. We also give an extension of the inequality valid in spaces satisfying a certain negative dependence property and give some applications.

Talagrand’s Inequality and Locality in Distributed Computing

We illustrate the use of Talagrand's inequality and an extension<br />of it to dependent random variables due to Marton for the analysis<br />of distributed randomised algorithms, specifically, for edge colouring<br />graphs.