Contingency tables are matrices with fixed row and column sums. They are in natural correspondence with bipartite multi-graphs with fixed degrees and can also be viewed as integer points in transportation polytopes. Counting and random sampling of contingency tables is a fundamental problem in statistics which remains unresolved in full generality.
In the talk, I will review both asymptotic and MCMC approaches, and then present a new Markov chain construction which provably works for sparse margins. I conclude with some curious experimental results and conjectures.
Joint work with Sam Dittmer.
This talk is independent of the first Erdős Lecture.