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

Repulsive Mean-Field Couplings and Self-Consistent Transfer Operators

  • Roberto Castorrini
  • Stefano Galatolo
  • Matteo Tanzi
Open at sourcePDFDOICite

Abstract

We study a one-dimensional self-consistent transfer operator generated by a repulsive mean-field coupling. The interaction admits a natural interpretation as a myopic relocation dynamics balancing congestion and uniformly distributed resources. Using the quantile representation of probability measures, combined with self-consistent transfer operators methods, we prove the existence and uniqueness of a physically relevant invariant measure for the system and characterize it explicitly through a nonlinear fixed-point equation. We then show that the corresponding finite-particle equilibrium converges to the continuum equilibrium with optimal order in Wasserstein distance and establish a quantitative thermodynamic limit.

Related

  1. On the dynamics of self-consistent transfer operators for interval maps with singularities
    Shadiyar Y. Altynbekov, Umrbek Olimov, Marks Ruziboev
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  2. Identifiability and Consistent Recovery for the Unnormalized Graph Laplace Operators
    Susovan Pal
    arXivPreprintCC BY 4.0Full textGeometry & topologyStatisticsarXiv
  3. Substochastic Path Operators for Refinement-Consistent Network Risks
    Luca Grilli, Domenico Santoro, Giacinto Angelo Sgarro
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref
  4. KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators
    Shengyu Yan, Jasmin Jelovica
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
  5. Instrumental Transfer Learning for Solution Operators
    Tongyu Li, Zhuoyuan Li, Ruoxu Tan
    arXivPreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{castorrini2026repulsive,
  title = {{Repulsive Mean-Field Couplings and Self-Consistent Transfer Operators}},
  author = {Roberto Castorrini and Stefano Galatolo and Matteo Tanzi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28664},
  eprint = {2609.28664},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28664},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Repulsive Mean-Field Couplings and Self-Consistent Transfer Operators
AU  - Roberto Castorrini
AU  - Stefano Galatolo
AU  - Matteo Tanzi
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28664
UR  - https://arxiv.org/abs/2609.28664
AB  - We study a one-dimensional self-consistent transfer operator generated by a repulsive mean-field coupling. The interaction admits a natural interpretation as a myopic relocation dynamics balancing congestion and uniformly distributed resources. Using the quantile representation of probability measures, combined with self-consistent transfer operators methods, we prove the existence and uniqueness of a physically relevant invariant measure for the system and characterize it explicitly through a nonlinear fixed-point equation. We then show that the corresponding finite-particle equilibrium converges to the continuum equilibrium with optimal order in Wasserstein distance and establish a quantitative thermodynamic limit.
ER  -