We study the Jensen--Shannon divergence (JSD) between transcript distributions induced by neighboring datasets in the shuffle model when each user applies a fixed local randomizer and a trusted shuffler releases the output histogram. Under a mild positivity assumption, we prove an explicit two-term asymptotic expansion where the leading term is chi-squared divergence divided by 8n. Binary randomized response and k-ary randomized response follow as corollaries. For multi-message protocols based on independent repetition, the leading coefficient becomes (1 + chi-squared)^m - 1. A fully explicit remainder control is provided in the appendix.

翻译：本研究探讨了在混洗模型中，当每个用户应用固定的本地随机化器且可信混洗器发布输出直方图时，相邻数据集诱导的转录分布之间的Jensen-Shannon散度（JSD）。在温和的正性假设下，我们证明了一个显式的两项渐近展开式，其中主导项为卡方散度除以8n。二元随机响应与k元随机响应可作为推论得出。对于基于独立重复的多消息协议，主导系数变为(1 + 卡方)^m - 1。附录中提供了完全显式的余项控制。