A Positive Corner Limit for Inverse Half-Powers of Vámos Quartics
Loading original first page…
Abstract
For each fixed parameter 0 < λ ≤ 64/27, this paper determines an anisotropic corner limit of the inverse Laplace distribution of a stable Vámos quartic raised to the power −1/2. The limit is an explicit positive density with arcsine slope sections. Convergence holds jointly in all scaled variables, including the variable where the exact partial inverse has a logarithmic singularity. The proof uses a modified Bessel partial inverse, differentiation to remove logarithmic counterterms and quantitative estimates for inversion on growing frequency regions. It also determines the first correction in the same joint distribution topology. The inverse of the stated stable Vámos family is treated as a distribution throughout.
Read the full paper in the original PDF.
Edition files
- Positive_corner_limit.pdf95.5 KiB · pdf
SHA-256
89095fa13a08f9166fe455a4a627789ad0b9615599885548e27f34f8789bf00a - Positive_corner_publication_package.zip102.7 KiB · package
SHA-256
106fd00e39937553bcc5c787281e371c3b8edbc6dd8b50340a30964046ba4c1b
Available editions
Research details
- Subjects
- Mathematics · Analysis and Spectral Theory
- Keywords
- Vámos quartics, inverse Laplace distributions, corner asymptotics, modified Bessel functions, hyperbolic polynomials
- Manuscript date
- 2026-10-23
- Reader reuse
- No additional permission granted
Scope
Joint corner convergence and its first distributional correction for each fixed positive stable parameter.
Disclosures
Author-posted preprint. AI-assisted internal research and verification were used.
Reproduction
The five-member package contains main.pdf, complete editable main.tex, reader instructions, citation metadata and checksums. Build with latexmk -pdf main.tex or tectonic main.tex using the standard packages declared in the source. The proof is analytic and the source compiles directly.
References and related resources
- M. F. Atiyah, R. Bott and L. Gårding, Lacunas for hyperbolic differential operators with constant coefficients I , Acta Math. 124 (1970), 109–189.
- Y. Baryshnikov and R. Pemantle, Asymptotics of multivariate sequences, part III: quadratic points, Adv. Math. 228 (2011), 3127–3206. arXiv:0810.4898, version 3.
- F. W. J. Olver et al., eds., NIST Digital Library of Mathematical Functions , §10.31 and §10.32, accessed October 23, 2026.
- S. Schubr, Sharp Stability and Geometric Classification of a Vámos Quartic Deformation , 2026, edition 1. Luminary Research Archive .
- A. D. Scott and A. D. Sokal, Complete monotonicity for inverse powers of some combinatorially defined polynomials, Acta Math. 213 (2014), 323–392. arXiv:1301.2449, expanded version 3.