Zoom: 937 905 8748 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 $mtimes n$ contingency tables when the marginals converge empirically to some fixed continuous margins on the unit interval as $n,mrightarrow infty$. 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.