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Peer-reviewedCC BYCommunications in Mathematical Physics

Continuum Polymer Measures Corresponding to the Critical 2d Stochastic Heat Flow

  • Jeremy Clark1
  • Barkat Mian2
  1. 1University of Mississippi Oxford, Oxford, MS, USA
  2. 2University of Tennessee, Knoxville, Knoxville, TN, USA
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Abstract

We construct continuum directed polymer measures corresponding to the critical 2d stochastic heat flow (2d SHF) introduced by Caravenna, Sun, and Zygouras in their recent article [Inventiones mathematicae 233 , 325–460 (2023)]. For this purpose, we prove a Chapman-Kolmogorov relation for the 2d SHF along with a related elementary conditional expectation formula. We explore some basic properties of the continuum polymer measures, with our main focus being on their second moments. In particular, we show that the form of their second moments is consistent with the family of continuum polymer measures, indexed by a disorder strength parameter, having a conditional Gaussian multiplicative chaos distributional interrelationship similar to that previously found in an analogous hierarchical toy model.

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Cite

BibTeXRIS
BibTeX
@article{clark2026continuum,
  title = {{Continuum Polymer Measures Corresponding to the Critical 2d Stochastic Heat Flow}},
  author = {Jeremy Clark and Barkat Mian},
  journal = {Communications in Mathematical Physics},
  year = {2026},
  month = jun,
  doi = {10.1007/s00220-026-05677-3},
  url = {https://doi.org/10.1007/s00220-026-05677-3},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Continuum Polymer Measures Corresponding to the Critical 2d Stochastic Heat Flow
AU  - Jeremy Clark
AU  - Barkat Mian
PY  - 2026
DA  - 2026/06/06
JO  - Communications in Mathematical Physics
DO  - 10.1007/s00220-026-05677-3
UR  - https://doi.org/10.1007/s00220-026-05677-3
AB  - We construct continuum directed polymer measures corresponding to the critical 2d stochastic heat flow (2d SHF) introduced by Caravenna, Sun, and Zygouras in their recent article [Inventiones mathematicae 233 , 325–460 (2023)]. For this purpose, we prove a Chapman-Kolmogorov relation for the 2d SHF along with a related elementary conditional expectation formula. We explore some basic properties of the continuum polymer measures, with our main focus being on their second moments. In particular, we show that the form of their second moments is consistent with the family of continuum polymer measures, indexed by a disorder strength parameter, having a conditional Gaussian multiplicative chaos distributional interrelationship similar to that previously found in an analogous hierarchical toy model.
SN  - 0010-3616
SN  - 1432-0916
ER  -