A Note on Asymptotic Enumeration of Contingency Tables with Non-Uniform Margins

Da Wu

Published 2020-10-11Version 1

In this short note, we compute the precise asymptotics for the number of contingency tables with non-uniform margins. More precisely, for parameter $n,\delta, B,C>0$, we consider the set of matrices whose first $[n^\delta]$ rows and columns have sum $[BCn]$ and the rest $n$ rows and columns have sum $[Cn]$. We compute the precise asymptotics of the cardinality of this set when $B<B_c=1+\sqrt{1+1/C}$ using the maximal entropy methods developed by Barvinok and Hartigan.