What does a random contingency table look like?

Understand

Let R=(r_1, ..., r_m) and C=(c_1, ..., c_n) be positive integer vectors such that r_1 +...

• + r_m=c_1 +...
• + c_n.
• We consider the set Sigma(R, C) of non-negative mxn integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure.