Weighted Switchings and Linear Corner Growth in Uniform Contingency Tables

Weighted Switchings and Linear Corner Growth in Uniform Contingency TablesAlper Ferudun, Mercury Software GmbH For a uniformly chosen nonnegative integer n-by-n matrix with both marginvectors (3n,n,...,n), the corner expectation has order n. An explicitfinite weighted-switching bound gives liminf E[X_11]/n >= 2-sqrt(2).The same corner law has total variation distance at least 1/4096 fromevery geometric distribution, including n-dependent choices of parameter.A general bound covers margins (L,t,...,t). The proof does not use anindependence approximation or a Markov-chain mixing theorem. This answers the linear-order question and gives a counterexample tounrestricted geometric entry approximation in OWR-5152-009. It does notassert the exact limiting mean, a Gaussian limit, or the full phasediagram. The fixed-base cloning results are not contradicted. English unrefereed preprint. Author affiliation: Mercury Software GmbH.OpenAI Codex assisted with derivation, literature review, computationalchecks and preparation. No independent review, formal verification,novelty certification or absolute priority claim. CC BY 4.0.