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

Effective Prescribed-Gradient Stability for Homogeneous Real-Stable Polynomials

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

For homogeneous real-stable polynomials of degree n in n variables, with nonnegative coefficients and value one at the all-ones vector, we give explicit positive rational constants in every fixed degree for a global prescribed-gradient coefficient reserve. On an explicitly specified closed neighborhood of the balanced gradient, the squarefree coefficient deficit dominates both centered-root dispersion and the coefficient ℓ^1 distance from the corresponding power of a linear form. The proof replaces the compactness step in the earlier qualitative theorem by a radial extension to a degree-drop boundary and a positive contraction dichotomy. An explicit positive map then corrects the gradient while preserving the centered factors. The bounds include singular dispersion and stable coefficient boundaries. We also obtain an explicit Frobenius-distance reserve for Hermitian mixed discriminants. The constants are deliberately coarse.

Read the full paper in the original PDF.