Let R = (r1, . . . , rm) and C = (c1, . . . , cn) be positive integer vectors such that r1 + . . .+ rm = c1 + . . .+ cn. We consider the set Σ(R, C) of non-negative m × n integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure. We prove that a random table D ∈ Σ(R, C) is close with high probability to a particular matrix (“t...