For large but finite source counts, the PDF of rescaled GWB characteristic strain squared follows the universal form N^{1/3} times the reflected map-Airy distribution evaluated at N^{1/3}(y-1), fully determined by the mean strain and a new cubic shot-noise scale.
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High initial eccentricities in stellar-mass black hole binaries produce a stochastic gravitational wave background distinguishable by LISA from quasi-circular models, enabling upper bounds on eccentricity and separation of environmental effects for dense gas.
Finite coherence during tidal Bohr crossings in axion clouds produces distinct, localized gravitational-wave waveforms and orbital responses in black-hole binaries.
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A practical theorem on gravitational-wave background statistics
For large but finite source counts, the PDF of rescaled GWB characteristic strain squared follows the universal form N^{1/3} times the reflected map-Airy distribution evaluated at N^{1/3}(y-1), fully determined by the mean strain and a new cubic shot-noise scale.