Georgia Institute of Technology College of Sciences

The discrete truncated moment problem considers the question whether given a discrete subsets $K \subset \mathbb{R}$ and a sequence of real numbers one can find a measure supported on $K$ whose (power) moments are exactly these numbers. The truncated moment is a challenging problem. We derive a minimal set of necessary and sufficient conditions. This simple problem is surprisingly hard and not treatable with known techniques. Applications to the truncated moment problem for point processes, the so-called relizability or representability problem are given. The relevance of this problem for statistical mechanics in particular the theory of classic liquids, is explained. This is a joint work with M. Infusino, J. Lebowitz and E. Speer.