Colloquia

In aggregation, clusters meet and irreversibly merge so that their average size grows continuously with time. This process describes, for example, making of jello and yogurt, raindrop formation in clouds, and the mass distribution of stars. I will present an elementary overview of cluster evolution in such aggregating systems. I begin by outlining the mean-field theory of aggregation and showing how scaling provides basic insights into long-time behavior. I will then discuss the intriguing relation between the cluster-size distribution and the first-passage probability of a random walk. Finally, I will discuss recent applications to traffic clustering and the distribution of wealth.