Adaptivity, Anchoring, and the Exact Oracle Complexity of Stochastic Fixed-Point Iterations 7HXP270BD0

URI	`m2://res/7HXP270BD0`
Kind	preprint
Creators	Yekini Shehu
Date	2026-09-26
MSC	49-XX, 90-XX, 93-XX, 94-XX
Subjects	arxiv math.OC, arxiv cs.IT, arxiv math.IT
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-09-26
Ids	arXiv 2610.00295

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
Oscillatory dichotomy, bounded-gap dense scales	statement	theorem 3.33	arxiv
Single-point stochastic oracle	definition	definition 2.1	arxiv
Doubling-window scheme: single-trajectory window adaptivity	statement	theorem 3.30	arxiv
Contraction-optimality of small $c$	statement	theorem 3.1	arxiv
High-probability exact rate, sub-Gaussian noise	statement	theorem 5.7	arxiv
Anchoring barrier	statement	lemma 5.16	arxiv
Geometric batching removes the logarithm	statement	theorem 5.5	arxiv
Union-class separation	statement	theorem 3.9	arxiv
Exact affine complexity	statement	corollary 5.4	arxiv
Dichotomy for general anchor densities	statement	theorem 3.14	arxiv
Kernel asymptotics	statement	lemma 3.4	arxiv
Universal rotation floor	statement	lemma 3.12	arxiv
Pointwise lacunarity law for Diophantine angles	conjecture	conjecture 3.22	arxiv
Rotation identity and floor	statement	lemma 3.5	arxiv
Universal anchor floor	statement	lemma 3.11	arxiv
Orbit transform: explicit form	statement	lemma 3.19	arxiv
Modulus ceiling	statement	corollary 5.12	arxiv
Impossibility of modulus-free gap certification	statement	theorem 5.19	arxiv
Stochastic parallel two-track scheme	statement	theorem 5.14	arxiv
Monotone-inclusion reduction and the optimal Hilbert rate	statement	theorem 4.8	arxiv
Anchoring cost	statement	theorem 5.17	arxiv
Master noise lemma	statement	lemma 4.1	arxiv
The oscillatory escape: the dichotomy fails under lacunary anchor concentration	statement	theorem 3.15	arxiv
The dichotomy is a single-instance phenomenon: fixed schedules	statement	corollary 3.27	arxiv
K1CKEFB94V	definition	definition	arxiv
Nonexpansive upper bound	statement	theorem 4.3	arxiv
Rotation decay law	statement	lemma 3.6	arxiv
Orbit small-ball	conjecture	conjecture 3.20	arxiv
Rotation lower envelope	statement	lemma 3.7	arxiv
Le\,Cam lower bound	statement	theorem 5.1	arxiv
Metric lacunarity law	statement	theorem 3.21	arxiv
Parallel two-track scheme: optimal on both regimes	statement	theorem 3.25	arxiv
Affine upper bound	statement	theorem 5.3	arxiv
Master noise lemma, contraction form	statement	lemma 4.6	arxiv
Repulsion and isolation of deep crossings	statement	lemma 3.18	arxiv
Gaussian two-point high-probability lower bound	statement	lemma 5.6	arxiv
Filtration	definition	definition 2.2	arxiv
High-probability version	statement	proposition 4.5	arxiv
Bounded-variance high probability: the exact rate, known modulus	statement	theorem 5.8	arxiv
Exact general-contraction complexity, known $\gamma$	statement	corollary 5.10	arxiv

Catalogue records

arxiv: 2610.00295 (work)
arxiv_text: 2610.00295 (work)