Exact JSD for the Continuous Gaussian Shuffle Model
Abstract
We derive the exact asymptotic expansion for Jensen-Shannon divergence in the Gaussian Shuffle Model: **JSD = SNR/(8n) − SNR²/(64n²) + O(n⁻³)** where SNR = μ²/σ² is the signal-to-noise ratio and n is the number of users. The negative second-order coefficient −1/64 contrasts with +3/64 for discrete Randomized Response, revealing a fundamental sign reversal between continuous and discrete local randomizers. Both cases unify under the leading-order formula JSD = χ²/(8n). **v2:** Fixed Corollary 5 — χ²/8 is a first-order approximation, not exact equality.
Fields of Study & Subjects
Privacy-Preserving Technologies in Data
Survey Sampling and Estimation Techniques
Internet Traffic Analysis and Secure E-voting
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 January 2026
- Language
- EN
- Document type
- Preprint