Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 39 min ago
PreprintCC BY 4.0arXiv

Unbalanced Minimal Matchings for Measurable Scale Invariant Costs on ℝd

  • Omer Angel
  • Nitya Gadhiwala
Open at sourcePDFDOICite

Abstract

Given red and blue points drawn from Poisson point processes of equal intensities, we match them by locally minimizing a cost function. In our paper, we identify all possible measurable cost functions on ℝd such that the resulting matching is scale invariant. Our cost functions can be asymmetrical, which we refer to as unbalanced cost functions. The investigation is motivated by arXiv:2012.07129 where the authors consider scale invariant cost functions with added regularity assumptions. Furthermore, we discuss how different the unbalanced matchings are compared to these more regular cost functions for points on ℝ.

Related

  1. Projections and minimal invariant subspaces in the Hardy space over the bidisk
    Marcos dos Santos Ferreira, João Marcos Ribeiro do Carmo
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
    Guido De Philippis, Luca Gennaioli, Alessandro Pigati +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  3. Regularity of critical immersions for scale-invariant curvature energies in even dimensions
    Tian Lan
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  4. Unbiased estimation of normalized scale-invariant indices under the Gamma distribution
    Roberto Vila, Helton Saulo, Felipe Quintino
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  5. SIMS: Scale-Invariant Merit-Function-Based Scalarization for Multi-Task Learning
    Zebin Chen, Fei Xing, Yang Chen +4
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{angel2026unbalanced,
  title = {{Unbalanced Minimal Matchings for Measurable Scale Invariant Costs on $\mathbbR^d$}},
  author = {Omer Angel and Nitya Gadhiwala},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19426},
  eprint = {2609.19426},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19426},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Unbalanced Minimal Matchings for Measurable Scale Invariant Costs on ℝ^d
AU  - Omer Angel
AU  - Nitya Gadhiwala
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19426
UR  - https://arxiv.org/abs/2609.19426
AB  - Given red and blue points drawn from Poisson point processes of equal intensities, we match them by locally minimizing a cost function. In our paper, we identify all possible measurable cost functions on ℝ^d such that the resulting matching is scale invariant. Our cost functions can be asymmetrical, which we refer to as unbalanced cost functions. The investigation is motivated by arXiv:2012.07129 where the authors consider scale invariant cost functions with added regularity assumptions. Furthermore, we discuss how different the unbalanced matchings are compared to these more regular cost functions for points on ℝ.
ER  -