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March 14, 2026Open Access

Universal Shuffle Asymptotics, Part III: Dominant-Block Quotient Geometry and Hybrid Gaussian–Compound-Poisson Limits in Finite-Alphabet Shuffle Privacy

Key Points

The research aims to establish a Lévy–Khintchine limit for neighboring shuffle experiments and explore privacy implications.
Analyzed dominant-block quotient geometry and neighboring shuffle experiments.
Applied Lévy–Khintchine limit to assess Gaussian factors and compound-Poisson jump fields.
Investigated geometric factors influencing privacy levels and certification speeds.
Found O(n⁻¹) projected Le Cam rate and hybrid rates showing compatibility conditions.
Achieved sharp O(n⁻¹/²) hybrid rate with boundary Berry–Esseen estimates.
Demonstrated that dominant-block overlap and boundary regularity control privacy and asymptotic behavior effectively.

Abstract

Final part of the trilogy. We prove a general Lévy–Khintchine limit for neighboring shuffle experiments: a common Gaussian factor on the dominant tangent space, a compound-Poisson jump field on the quotient carrying the full neighboring shift Δ, O(n⁻¹) projected Le Cam rate, privacy-curve convergence in regular regimes, a strong-boundary obstruction, sharp O(n⁻¹/²) hybrid rate with a compatibility condition restoring O(n⁻¹), and boundary Berry–Esseen giving O(c) Poisson-to-Gaussian proximity. A numerical companion demonstrates that dominant-block overlap, cross/native split-law compatibility, and boundary regularity are the three geometric levers controlling privacy level, certification speed, and asymptotic safety. Completes the series with Parts I–II.

Universal Shuffle Asymptotics, Part III: Dominant-Block Quotient Geometry and Hybrid Gaussian–Compound-Poisson Limits in Finite-Alphabet Shuffle Privacy

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Abstract

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