Axel Janson: Dimension-aware CLT convergence rates for sample polyspectra via Malliavin–Stein

Polyspectra play a central role in orbit recovery problems such as multi-reference alignment, providing shift-invariant information about an underlying signal. Motivated by likelihood-based inference for sample polyspectra, I present a quantitative central limit theorem for high-dimensional collections of these statistics under a Gaussian observation model. The theorem yields explicit, dimension-aware bounds for a multivariate Gaussian approximation, clarifying how the error depends on sample size, signal dimension, noise level, signal strength, and tensor order. I will sketch the main ideas, combining finite chaos expansions with a streamlined Malliavin–Stein argument that reduces the analysis to controlling contraction terms, and discuss how to interpret the resulting rates.