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Counting contingency tables

Algebra & Discrete Mathematics

Speaker: Prof. Igor Pak, Univ. of California, Los Angeles
Location: 1147 Math Science Building
Start time: Mon, Apr 8 2019, 12:10PM

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 will conclude with the ongoing work on the phase transition for certain Barvinok margins.

Joint work with Sam Dittmer.