Tutte Colloquium - Peter Winkler

Title: Sets that Support a Joint Distribution

Abstract: Given a closed set on the plane and two probability distributions on the real line, when are there random variables with the given distributions whose joint distribution is supported by the given set?

We consider both discrete and continuous distributions. In the discrete case, what is needed is a full, nowhere-zero flow in a node-weighted bipartite graph. In the continuous case, the problem is equivalent to asking which sets in the unit square can support a permuton---AKA, a doubly-stochastic measure.

Joint work with Chris Coscia and Martin Tassy.