Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

154 papers
Browse papers
  1. Self-concordance and allocation for spatial power sumsScott SchubrEdition 3 · 2026-11-01 Public
  2. Sharp all-times heat-content comparison and concentration on compact metric graphsScott SchubrEdition 3 · 2026-11-01 Public
  3. Energy-Filtered Dynamical Localization in Constructive Dirichlet TowersScott SchubrEdition 3 · 2026-11-01 Public
  4. Degree-dependent minimax laws for Gaussian factorial momentsScott SchubrEdition 2 · 2026-11-01 Public
  5. A sharp lower bound for adjacent-edge correlations in random subtreesScott SchubrEdition 4 · 2026-11-01 Public
  6. Sharp transport identification with unknown Gaussian covarianceScott SchubrEdition 3 · 2026-11-01 Public
  7. Statistical inference for empirical heat-kernel Sinkhorn metricsScott SchubrEdition 5 · 2026-11-01 Public
  8. First-Hit Stopping and Bias-Corrected Score Inference in Dimension ThreeScott SchubrEdition 5 · 2026-11-01 Public
  9. Sharp Wasserstein Stability for Gaussian Deconvolution of Log-Concave LawsScott SchubrEdition 4 · 2026-11-01 Public
  10. Exact low-brightness minimax risk for quartic Gaussian energyScott SchubrEdition 1 · 2026-11-01 Public
  11. Sharp estimation costs for thermal Gaussian energies with known backgroundScott SchubrEdition 1 · 2026-11-01 Public
  12. Sharp calibration costs for high-order thermal Gaussian energiesScott SchubrEdition 1 · 2026-11-01 Public
  13. A sharp flatness transition for critical heat traces in twisted tubesScott SchubrEdition 1 · 2026-11-01 Public
  14. Prescribed-Gradient Coefficient Stability for Lorentzian PolynomialsScott SchubrEdition 1 · 2026-11-01 Public
  15. Closure correlations in paving and low-corank matroidsScott SchubrEdition 1 · 2026-11-01 Public
  16. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 4 · 2026-11-01 Public
  17. Polynomial inertia of signed measures with negative intervalsScott SchubrEdition 3 · 2026-11-01 Public
  18. Holomorphic certification on real subspacesScott SchubrEdition 3 · 2026-11-01 Public
  19. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 5 · 2026-11-01 Public
  20. Optimal unbiased Gaussian quantum estimation and the cost of unknown squeezingScott SchubrEdition 1 · 2026-11-01 Public
  21. Optimal unbiased estimation of polynomial energies in thermal Gaussian statesScott SchubrEdition 3 · 2026-10-31 Public
  22. Unrestricted Half-Power Obstruction and Polynomial Certificates for the Vámos QuarticScott SchubrEdition 5 · 2026-10-31 Public
  23. Dimension thresholds for log-concavity of normalized mixed momentsScott SchubrEdition 3 · 2026-10-31 Public
  24. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 2 · 2026-10-31 Public
PublicEdition 2

Quantitative Null-Space Compression for a Weighted Weil Operator

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

We study a fixed minimal weighted realization H=A+B of the constrained Weil form, with nonnegative logarithmic reference A and the complete bounded paired arithmetic perturbation B. For every 0<τ≤1, explicit Fourier-band moments cut out a finite-codimensional subspace of the entire operator kernel on which both A and A^(1/2) have norm at most τ. The number n(τ) of observations satisfies log n(τ) = O(√(1+log(1/τ)) log(3+log(1/τ))). Consequently AΠ_Y and A^(1/2)Π_Y belong to every Schatten class for every closed Y⊆ker H. The proof combines two complete phase-space tails, a finite-rank real-phase Taylor approximation, and the exact null equation. We also give norm estimates for finite null deflation, a full residual-Gram receiving certificate, an explicit weighted bound H≥-99I/100, and a multiplicity obstruction to identifying the derivative-null closure with the whole kernel. The observations are explicit; the projection inside the unknown kernel is not computationally constructed.

Read the full paper in the original PDF.