Spectral Costs of Multinomial and Residual Resampling in High-Dimensional Particle Ensembles: A Free-Probability Analysis
Resampling is the standard remedy against weight degeneracy in particle filters, yet its effect on the spectrum of the particle second-moment matrix is poorly understood. We study a single resampling step for a d-dimensional ensemble of N particles with d/N -> c. For any unbiased scheme, the resampled empirical second-moment matrix dominates its pre-resampling counterpart in conditional convex order, while the conditional mean is preserved; the excess second spectral moment equals the Frobenius energy of the resampling perturbation. For multinomial resampling, the empirical count law converges to the mixed-Poisson law determined by the limiting weight law. For residual resampling, the cou...
| Authors | Deming Song, Chi Kin Lam |
|---|---|
| Primary category | math.ST |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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