Spectral Costs of Multinomial and Residual Resampling in High-Dimensional Particle Ensembles: A Free-Probability Analysis H29YHXQZV6

URI	`m2://res/H29YHXQZV6`
Kind	preprint
Creators	Deming Song, Chi Kin Lam
Date	2026-10-12
MSC	62-XX
Subjects	arxiv math.ST, arxiv cs.LG, arxiv stat.TH
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-10-12
Ids	arXiv 2610.16680

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Exact second spectral moment cost	statement	proposition 4	arxiv
Asymptotic rank-preservation ordering	statement	corollary 23	arxiv
Finite-sample Frobenius ordering	statement	corollary 25	arxiv
Spectral moments and the exact increment	statement	proposition 15	arxiv
Information content of the effective sample size	statement	proposition 16	arxiv
Zero-eigenvalue mass and rank loss	statement	proposition 14	arxiv
Conditional unbiasedness identity	statement	lemma 1	arxiv
Conditional convex order	definition	definition 2	arxiv
BNKX33RY7B	statement	theorem	arxiv
EV50DRKZBH	statement	theorem	arxiv
Classification of residual limits under $\rho=\delta_1$	statement	theorem 10	arxiv
General population spectrum; Gaussian case	statement	theorem 12	arxiv
Residual second-moment cost	statement	proposition 22	arxiv
Limiting spectral distribution; identity population	statement	theorem 11	arxiv
Spectral edges and support	statement	proposition 19	arxiv
Scheme-agnostic Jensen principle	statement	theorem 3	arxiv
N927TPZ8YJ	statement	lemma	arxiv
Covariance-side spectral map	definition	definition 8	arxiv
Residual zero atom and threshold	statement	corollary 21	arxiv
Residual spectral transform	statement	theorem 20	arxiv
Multinomial count law	statement	theorem 7	arxiv
Exact-uniform-weight contrast	statement	corollary 24	arxiv
SMGT7M7Q87	statement	theorem	arxiv
Asymptotic decrease of the effective dimension	statement	corollary 17	arxiv
Rank-and-spectral-gap transition	statement	theorem 18	arxiv
Population-averaged cost and diffuse-weight limit	statement	proposition 6	arxiv
W5JAJDSCZ3	statement	theorem	arxiv
XGV86WA1S6	statement	theorem	arxiv
Residual count law	statement	theorem 9	arxiv

Catalogue records

arxiv: 2610.16680 (work)
arxiv_text: 2610.16680 (work)