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Weak universality of global dynamics for the fractional hyperbolic Φ43-model

  • Ruoyuan Liu
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Abstract

We continue the study of weak universality for the fractional hyperbolic Φ43-model initiated by Tzvetkov, Wang, and the author (2023). In this work, we establish weak universality in a regime where the associated Gibbs measure is mutually singular with respect to the underlying Gaussian measure. We first investigate the weak convergence of the Gibbs measures associated with macroscopic models to the fractional Φ43-measure constructed by Tzvetkov, Wang, and the author (2023). We then obtain a structured representation for these Gibbs measures via the stochastic quantization method. Finally, we prove dynamical weak universality for the fractional hyperbolic Φ43-model by using an extended second order expansion and exploiting the invariance of the Gibbs measures.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026weak,
  title = {{Weak universality of global dynamics for the fractional hyperbolic $Φ^4_3$-model}},
  author = {Ruoyuan Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15135},
  eprint = {2610.15135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15135},
}
RIS
TY  - UNPB
TI  - Weak universality of global dynamics for the fractional hyperbolic Φ^4_3-model
AU  - Ruoyuan Liu
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.15135
UR  - https://arxiv.org/abs/2610.15135
AB  - We continue the study of weak universality for the fractional hyperbolic Φ^4_3-model initiated by Tzvetkov, Wang, and the author (2023). In this work, we establish weak universality in a regime where the associated Gibbs measure is mutually singular with respect to the underlying Gaussian measure. We first investigate the weak convergence of the Gibbs measures associated with macroscopic models to the fractional Φ^4_3-measure constructed by Tzvetkov, Wang, and the author (2023). We then obtain a structured representation for these Gibbs measures via the stochastic quantization method. Finally, we prove dynamical weak universality for the fractional hyperbolic Φ^4_3-model by using an extended second order expansion and exploiting the invariance of the Gibbs measures.
ER  -