On the number of contingency tables and the independence heuristic. Issue 1 (28th February 2022) - Lyu, Hanbaek; Pak, Igor
Abstract: We obtain sharp asymptotic estimates on the number of n × n $n × n$ contingency tables with two linear margins C n $Cn$ and B C n $BCn$ . The results imply a second‐order phase transition on the number of such contingency tables, with a critical value at B c : = 1 + 1 + 1 / C $B_{c}:=1 + \sqrt {1+1/C}$ . As a consequence, for B > B c $B>B_{c}$, we prove that the classical independence heuristic leads to a large undercounting.