Advances in the analysis of random structures and their applications: relationships among models

The project will demonstrate the importance of relationships among models of random structures, and between these and deterministic structures. It introduces novel approaches to apply probability theory and continuous mathematics to random graph theory, random networks and probabilistic Combinatorics, areas of growing importance in algorithmic Computer Science. Some of the particular goals are fundamental problems whose solution will lead to breakthroughs in understanding the nature of random structures. Others, at the interface of mathematics and computer science, can lead to novel algorithms for balancing the load of disks or computers, or to new understanding of the inherent difficulties of the computational solutions of problems.