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Characterizing optimal sampling of binary contingency tables via the configuration model

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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 equation image goes to . Our finding shows surprising differences from recent results for binary symmetric contingency tables. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012

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