Skip to content
DraconiticResearch
Search Sources API
182,469 studies31 sourcesUpdated 17 min ago
PreprintCC BY-SA 4.0arXiv

Approximate Uniformity in Finite Convolution Models

  • Nilava Metya
  • Satyaki Mukherjee
Open at sourcePDFDOICite

Abstract

The problem of the uniform law being a sum of two independent distributions has been well studied. Here, we study the approximation of the uniform law to a sum of two distributions with fixed support, under the following discrepancies: the Manhattan distance, the Euclidean distance, the forward Kullback--Leibler divergence and the Wasserstein-one distance based on the line metric. The problem of membership of the uniform law in this model has been well studied. Explicit results are obtained in two models, one where one of the distributions is a Bernoulli and the other when both distributions have the same support, including one conjecture. Finally, we show an application of our reconstruction method to a recent conjecture about the coding capacity of an additive noise channel.

Related

  1. New Construction of Power Functions with Low c-Differential Uniformity over Finite Fields
    Zhiye Yang, Yan Wang, Keqin Feng
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  2. The twisted convolution identity and ghost r-SICs from finite quantum dilogarithms
    Marcus Appleby, Steven T. Flammia, Gene S. Kopp
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  3. Uniformity theory of weighted composites
    Marcelo Epstein, Mohammadjavad Javadi
    arXivPreprintCC BY 4.0Full textMathematical physicsCondensed matterarXiv
  4. Profinite recognition of uniformity
    Holger Kammeyer
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Norm properties of quantum uniformity measures
    Berke Ünal
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{metya2026approximate,
  title = {{Approximate Uniformity in Finite Convolution Models}},
  author = {Nilava Metya and Satyaki Mukherjee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38243},
  eprint = {2609.38243},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38243},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Approximate Uniformity in Finite Convolution Models
AU  - Nilava Metya
AU  - Satyaki Mukherjee
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38243
UR  - https://arxiv.org/abs/2609.38243
AB  - The problem of the uniform law being a sum of two independent distributions has been well studied. Here, we study the approximation of the uniform law to a sum of two distributions with fixed support, under the following discrepancies: the Manhattan distance, the Euclidean distance, the forward Kullback--Leibler divergence and the Wasserstein-one distance based on the line metric. The problem of membership of the uniform law in this model has been well studied. Explicit results are obtained in two models, one where one of the distributions is a Bernoulli and the other when both distributions have the same support, including one conjecture. Finally, we show an application of our reconstruction method to a recent conjecture about the coding capacity of an additive noise channel.
ER  -