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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 $$extract_itex$$mtimesn$$/extract_itex$$ contingency tables when the marginals converge empirically to some fixed continuous margins on the unit interval as $$extract_itex$$n,mrightarrowinfty$$/extract_itex$$. 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.