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Exact detection threshold of the packing test

math.ST · 2026-08-01 · accept · novelty 7.0

The packing test detects FvML deviations only when the concentration kappa is of order p^{3/4}/(log n)^{1/4}, and Watson deviations only when p-2*kappa is of order sqrt(p log n), with a discontinuous phase transition in the second-order scaling.

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  • Exact detection threshold of the packing test math.ST · 2026-08-01 · accept · none · ref 1989

    The packing test detects FvML deviations only when the concentration kappa is of order p^{3/4}/(log n)^{1/4}, and Watson deviations only when p-2*kappa is of order sqrt(p log n), with a discontinuous phase transition in the second-order scaling.