Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 32 min ago
PreprintarXiv licencearXiv

On the maximum visibility in a ball through the vacant set of Poissonian obstacles

  • Yingxin Mu
  • Artem Sapozhnikov
Open at sourcePDFDOICite

Abstract

We study the maximum visibility in a ball inside the vacant set of three obstacle models in ℝd with slow decay of spatial correlations and disparate obstacle geometries: Poisson Boolean models with general i.i.d. radii distributions, Poisson cylinders and Brownian interlacements. Let Mr be the maximum distance between points x and y in the ball B(r) such that x is visible from y. We prove that Mr divided by qr converges in probability to an explicit model dependent constant, where qr=log r, except for the Brownian interlacements in dimension d=3, where qr = log rloglog r.

Related

  1. Efficient Importance Sampling of Brownian Motion Avoiding Poissonian Obstacles for Long Time
    Jose Blanchet, Paul Dupuis, Hao Liu
    arXivPreprintCC BY 4.0Full textProbabilityarXiv
  2. Decompositions of CSBPs via Poissonian Intertwining
    Clément Foucart, Olivier Hénard
    ALEA : Latin American Journal of Probability and Mathematical StatisticsPeer-reviewedLicence not statedGeneral mathematicsHAL
  3. Metric Poissonian Pair Correlation Property Part 1: The Case n+log n
    Bo Tan, Zhen Zhang, Qing-Long Zhou
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Poissonian pair correlations for the three-particle Sutherland model
    Christopher Lutsko
    arXivPreprintarXiv licenceFull textAlgebra & number theoryMathematical physicsarXiv
  5. Poissonian Pair Correlation for Bernoulli Orbits
    Bo Tan, Zhen Zhang, Qing-Long Zhou
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{mu2026maximum,
  title = {{On the maximum visibility in a ball through the vacant set of Poissonian obstacles}},
  author = {Yingxin Mu and Artem Sapozhnikov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11690},
  eprint = {2609.11690},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11690},
}
RIS
TY  - UNPB
TI  - On the maximum visibility in a ball through the vacant set of Poissonian obstacles
AU  - Yingxin Mu
AU  - Artem Sapozhnikov
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11690
UR  - https://arxiv.org/abs/2609.11690
AB  - We study the maximum visibility in a ball inside the vacant set of three obstacle models in ℝ^d with slow decay of spatial correlations and disparate obstacle geometries: Poisson Boolean models with general i.i.d. radii distributions, Poisson cylinders and Brownian interlacements. Let M_r be the maximum distance between points x and y in the ball B(r) such that x is visible from y. We prove that M_r divided by q_r converges in probability to an explicit model dependent constant, where q_r=log r, except for the Brownian interlacements in dimension d=3, where q_r = log rloglog r.
ER  -