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Peer-reviewedCC BYJournal of the European Mathematical Society

Parabolic stochastic quantisation of the fractional Φ43 model in the full subcritical regime

  • Paweł Duch1,2
  • Massimiliano Gubinelli3
  • Paolo Rinaldi4
4 affiliations
  1. 1Adam Mickiewicz University in Poznań, Poland
  2. 2EPFL, Lausanne, Switzerland
  3. 3University of Oxford, UK
  4. 4Università di Pavia, Italy
Open at sourceDOICite

Abstract

We present a construction of the measure of the fractional \Phi^{4} Euclidean quantum field theory on \mathbb{R}^{3} in the full subcritical regime via parabolic stochastic quantisation. Our approach is based on a truncated flow equation for the effective description of the model at sufficiently small scales and on coercive estimates for the nonlinear stochastic partial differential equation describing the interacting field. The constructed measure is translation invariant, reflection positive, and has quartic exponential tails.

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Cite

BibTeXRIS
BibTeX
@article{duch2026parabolic,
  title = {{Parabolic stochastic quantisation of the fractional $\Phi^4_3$ model in the full subcritical regime}},
  author = {Paweł Duch and Massimiliano Gubinelli and Paolo Rinaldi},
  journal = {Journal of the European Mathematical Society},
  year = {2026},
  month = oct,
  doi = {10.4171/jems/1816},
  url = {https://doi.org/10.4171/jems/1816},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Parabolic stochastic quantisation of the fractional Φ^4_3 model in the full subcritical regime
AU  - Paweł Duch
AU  - Massimiliano Gubinelli
AU  - Paolo Rinaldi
PY  - 2026
DA  - 2026/10/12
JO  - Journal of the European Mathematical Society
DO  - 10.4171/jems/1816
UR  - https://doi.org/10.4171/jems/1816
AB  - We present a construction of the measure of the fractional \Phi^{4} Euclidean quantum field theory on \mathbb{R}^{3} in the full subcritical regime via parabolic stochastic quantisation. Our approach is based on a truncated flow equation for the effective description of the model at sufficiently small scales and on coercive estimates for the nonlinear stochastic partial differential equation describing the interacting field. The constructed measure is translation invariant, reflection positive, and has quartic exponential tails.
SN  - 1435-9855
SN  - 1435-9863
ER  -