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  1. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  2. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  3. Single-copy learning of noisy stabilizers by certified filteringScott SchubrEdition 2 · 2026-10-27 Public
  4. Exponential growth of sparse Euler products and normal graded domainsScott SchubrEdition 2 · 2026-10-27 Public
  5. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp Stability and Geometric Classification of a Vámos Quartic DeformationScott SchubrEdition 2 · 2026-10-27 Public
  7. Strong permanent inequalities for cycles and a class of single-chord supportsScott SchubrEdition 2 · 2026-10-27 Public
  8. Sharp Quadratic Smoothing for Truncated Simplex SumsScott SchubrEdition 2 · 2026-10-27 Public
  9. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
  10. Three-point positivity for weighted products of Riemann theta density powersScott SchubrEdition 2 · 2026-10-27 Public
  11. Strong permanent inequalities on three chorded seven-cycle supportsScott SchubrEdition 2 · 2026-10-27 Public
  12. Coupled permanent cofactors: sharp occupation bounds and compensation geometryScott SchubrEdition 11 · 2026-10-27 Public
  13. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  15. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  16. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  17. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  18. Compact capture and protected bridges on the Koras–Russell cylinderScott SchubrEdition 2 · 2026-10-27 Public
  19. Dimension-dependent holomorphic certificate degrees on zero-sum hyperplanesScott SchubrEdition 2 · 2026-10-27 Public
  20. Admissible kernel lifts with positive endpoint forms and nonreal Fourier zerosScott SchubrEdition 2 · 2026-10-27 Public
  21. Global finite-depth stability and nonreal zeros of admissible Fourier transformsScott SchubrEdition 2 · 2026-10-27 Public
  22. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  23. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  24. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

Fourier computation of empirical diffusion metrics

Scott Schubr

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Abstract

We give a finite Fourier algorithm for computing empirical diffusion-metric entries together with their joint uncertainty estimates. The metric is defined through an inverse weighted Laplacian and estimated by empirical heat-kernel Sinkhorn normalization. For a fixed smooth, strictly positive density on a fixed-dimensional flat torus and fixed smooth test functions, the algorithm preserves the exact estimator's population-centered Gaussian limit, joint covariance consistency and ordinary nonparametric bootstrap. For every fixed eta > 0, its deterministic work is O(n^(1+eta)) in the exact-real model, using sufficiently high fixed-order bias extrapolation. The proof controls the closing spectral gap as bandwidth decreases, the actual normalization iterations, and the errors in both the inverse metric and its influence covariance under the original empirical weights. Positive Fourier features and reduced linear solves provide the algorithm. The work bound includes feature-Gram construction and factorization; explicit finite schedules illustrate the resulting resource counts.

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