Characterizing optimal sampling of binary contingency tables via the configuration model. Issue 2 (13th February 2012) - Blanchet, Jose; Stauffer, Alexandre
Abstract A binary contingency table is an m × n array of binary entries with row sums r = (r1, …, rm) and column sums c = (c1, …, cn). The configuration model generates a contingency table by considering ri tokens of type 1 for each row i and cj tokens of type 2 for each column j, and then taking a uniformly random pairing between type‐1 and type‐2 tokens. We give a necessary and sufficient condition so that the probability that the configuration model outputs a binary contingency table remains bounded away from 0 as <![CDATA[\documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{align*}N=\sum_{i=1}^m r_i=\sum_{j=1}^n c_j\end{align*} \end{document}]]> <inline-graphic xlink:href="ark:/27927/pgg1s17r0km" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> goes to ∞. Our finding shows surprising differences from recent results for binary symmetric contingency tables. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012