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To derive a second-order asymptotic expansion for Jensen–Shannon divergence in the unbundled shuffle model.

January 23, 20260 citationsOpen Access

Exact Second-Order Jensen–Shannon Asymptotics in the Unbundled Shuffle Model

Key Points

To derive a second-order asymptotic expansion for Jensen–Shannon divergence in the unbundled shuffle model.
Analytical proof techniques were used to develop the expansion.
The model focuses on unbundled multi-message shuffling.
Complete control over the remainder term was achieved.
The analysis reveals an exponential separation between bundled and unbundled shuffling.
Bundling amplifies divergence exponentially with the number of messages per user.
In contrast, unbundled shuffling maintains linear scaling.

Abstract

We derive a sharp second-order asymptotic expansion for the Jensen–Shannon divergence in the unbundled multi-message shuffle model. The proof is fully analytic and provides complete control of the remainder term. The results show an exponential separation between bundled and unbundled shuffling: bundling amplifies divergence exponentially in the number of messages per user, while unbundled shuffling preserves linear scaling.

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Cite This Study

Alex B. Shvets (2026) studied this question.

synapsesocial.com/papers/69731089c8125b09b0d20350 https://doi.org/https://doi.org/10.5281/zenodo.18331729