Universal Shuffle Asymptotics, Part II: Non-Gaussian Limits for Shuffle Privacy — Poisson, Skellam, and Point Process Regimes

Part II of the Universal Shuffle Asymptotics series. Characterizes the first universality-breaking frontier for shuffle differential privacy: critical sequences of increasingly concentrated local randomizers where classical Lindeberg conditions fail and the shuffle score exhibits rare macroscopic jumps. Main results: (1) Poisson-shift limit experiment for the canonical neighboring pair when exp(ε₀(n))/n → c², with explicit O(1/n) Le Cam convergence rate and a support-mismatch δ-floor; (2) Skellam-shift limit for proportional compositions k/n → π ∈ (0,1), with disappearance of the δ-floor away from boundary compositions; (3) multivariate Poisson point process / compound-Poisson limit for general finite alphabets under a sparse-error critical regime, yielding explicit limiting (ε,δ) curves as Poisson series; (4) a three-regime phase diagram (sub-critical Gaussian, critical Poisson/Skellam/PPP, super-critical no privacy) unifying Parts I and II. All convergence results are at the level of binary experiments and Le Cam distance with explicit total-variation bounds. Includes reproducible Python code for numerical illustrations. Companion to Part I (Sharp Privacy Analysis in the Gaussian Regime).