Skip to content
DraconiticResearch
Search Sources API
190,332 studies31 sourcesUpdated 40 min ago
PreprintarXiv licencearXiv

Arithmetic probability measures

  • Mayuresh Londhe
Open at sourcePDFDOICite

Abstract

We consider probability measures on compact subsets of the complex plane arising as limiting distributions of Galois conjugates of certain algebraic integers. These measures are characterized by infinitely many integral inequalities, one for each nonzero integer polynomial. We study a broad family of measures given by particular convex combinations of harmonic and equilibrium measures. We then show that, for measures in this family, it suffices to verify two conditions to guarantee all the required inequalities. Under additional arithmetic constraints on the underlying compact sets, we further show that the infinite collection of inequalities is equivalent to checking the inequalities associated with two explicitly specified integer polynomials.

Related

  1. Generalized Bratteli diagrams without probability tail invariant measures
    Andrew Barsky, Sergey Bezuglyi
    arXivPreprintCC BY 4.0Full textDynamical systemsProbabilityarXiv
  2. An Improved Fractal Analysis of Directional Densities for Borel Probability Measures
    Ines Ben Omrane, Abdulmajeed Alqasem, Mourad Ben Slimane +1
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  3. Invariant probability measures for path-dependent regime-switching processes
    Jianrui Li, Jinghai Shao
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Grünbaum's inequality for Gaussian and convex probability measures
    Matthieu Fradelizi, Dylan Langharst, Jiaqian Liu +2
    HALPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsHAL
  5. Invariant probability measures on holomorphic functions on the unit disk
    Oleg Ivrii, Uri Kreitner
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{londhe2026arithmetic,
  title = {{Arithmetic probability measures}},
  author = {Mayuresh Londhe},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03939},
  eprint = {2609.03939},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03939},
}
RIS
TY  - UNPB
TI  - Arithmetic probability measures
AU  - Mayuresh Londhe
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03939
UR  - https://arxiv.org/abs/2609.03939
AB  - We consider probability measures on compact subsets of the complex plane arising as limiting distributions of Galois conjugates of certain algebraic integers. These measures are characterized by infinitely many integral inequalities, one for each nonzero integer polynomial. We study a broad family of measures given by particular convex combinations of harmonic and equilibrium measures. We then show that, for measures in this family, it suffices to verify two conditions to guarantee all the required inequalities. Under additional arithmetic constraints on the underlying compact sets, we further show that the infinite collection of inequalities is equivalent to checking the inequalities associated with two explicitly specified integer polynomials.
ER  -