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Indeed, conditionally on eT1, eT2, the event n X⊤ 1 X2 >t◦ n o is equivalent to √ d·Z> √ d· t◦ n− eT1eT2 q 1− eT 2 1 q 1− eT 2 2

:= ρn π · L (an−α 1α2) √ 2πL ×exp ( −L " ρn(α2 1 +α 2 2)+ α4 1 +α 4 2 4 + 1 2(an−α 1α2)2 #) ×L (an−α1α2)/(2An)·exp ( −an−α 1α2 2an x ) · 2003

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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 6

    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.