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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.