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  1. Positive Operator Cocycles in Shrinking CorridorsScott SchubrEdition 2 · 2026-10-31 Public
  2. Coherence thresholds for optimal-rate stabilizer purity testingScott SchubrEdition 2 · 2026-10-31 Public
  3. Spectral escape for interacting and coalescing signed potential formsScott SchubrEdition 5 · 2026-10-30 Public
  4. Large negative subspaces for positive Euler deformationsScott SchubrEdition 3 · 2026-10-30 Public
  5. Fourier computation of empirical diffusion metricsScott SchubrEdition 2 · 2026-10-30 Public
  6. Purity frontiers and optimal copy complexity for qutrit stabilizer measurementsScott SchubrEdition 2 · 2026-10-30 Public
  7. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 3 · 2026-10-30 Public
  8. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 4 · 2026-10-30 Public
  9. Mixing-weight entropy concavity near the Gaussian below one-half signalScott SchubrEdition 3 · 2026-10-30 Public
  10. Covariance-Spectrum Certificates for Homogeneous Stable Count LawsScott SchubrEdition 8 · 2026-10-30 Public
  11. Relative tail payment and spectral enclosuresScott SchubrEdition 1 · 2026-10-29 Public
  12. Joint inclusion bounds for random greedy matroid basesScott SchubrEdition 1 · 2026-10-29 Public
  13. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  14. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  15. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  16. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  17. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  18. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  19. Exact-rank quadratic correlation: a phase-compatible Clique reductionScott SchubrEdition 1 · 2026-10-27 Public
  20. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  21. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  22. Independent Squares and Average-Radius Obstructions for Linear CodesScott SchubrEdition 2 · 2026-10-27 Public
  23. An explicit quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  24. A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 1

Prescribed-Gradient Coefficient Stability for Lorentzian Polynomials

Scott Schubr

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Abstract

For normalized Lorentzian polynomials of degree n in n variables, we prove that the power of a linear form with prescribed gradient is the unique minimizer of the squarefree coefficient whenever that gradient is sufficiently close to the all-ones vector. The coefficient excess controls the full coefficient ℓ¹ distance, uniformly in each fixed degree. The proof gives an explicit separation bound for the cone determined by the transverse quadratic derivatives at the balanced power. This bound also yields an explicit local stability estimate when both gradient and polynomial are close to that power. Variable splitting extends the result to positive integer compositions, and volume polynomials give a mixed-volume coefficient stability bound.

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