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Uniform random contingency tables nonnegative integer matrices of a given size, chosen uniformly at random given some fixed marginals. They also correspond to uniform random bipartite graphs with give degree sequences. In this talk, we develop a limit theory of uniform mtimesn contingency tables when the marginals converge empirically to some fixed continuous margins on the unit interval as n,mrightarrowinfty. We show that the uniform contingency tables are exponentially concentrated and converge weakly to a deterministic joint distribution on the unit square, which is characterized as the unique solution of some associated convex optimization problem.
This is a joint work with Sumit Muhkerjee.