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We investigate the properties of uniform doubly stochastic random matrices,that is non-negative matrices conditioned to have their rows and columns sum to1. The rescaled marginal distributions are shown to converge to exponentialdistributions and indeed even large sub-matrices of side-length$o(n^{1/2-\epsilon})$ behave like independent exponentials. We determine thelimiting empirical distribution of the singular values the the matrix. Finallythe mixing time of the associated Markov chains is shown to be exactly 2 withhigh probability.

Properties of Uniform Doubly Stochastic Matrices