Deterministic Randomness

I will discuss processes that combine determinism and randomness. The main focus of this talk will be the analysis of an algorithm using "power of two choices" techniques to create a cost-minimizing allocation. My analysis of this algorithm uses ideas from differential equations, random walks, and some new approaches. I also survey other applications and problems in the field. The balls-and-bins allocation algorithm of Azar, Broder, Karlin and Upfal is one of the first applications of this technique. I discuss their work as well as related problems in Achlioptas random graphs, queuing theory, and analysis of physical processes.