Universal Asymptotics for Jensen–Shannon Divergence under Shuffling

arXiv:2602.09029v1 Announce Type: new
Abstract: 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.