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PreprintCC BY 4.0arXiv

A universality result for the critical 2d stochastic heat flow

  • Hindy Drillick
  • Jonathan Hou
  • Shalin Parekh
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Abstract

For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical 2d stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The class of discrete models we consider includes random walks in space-time random environments with finite-range jumps, and directed polymer models with finite-range spatial correlations. The class of continuum models we consider includes several distinct types of linear-multiplicative stochastic PDEs whose driving noise is Gaussian with a smooth and compactly supported covariance kernel.

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Cite

BibTeXRIS
BibTeX
@misc{drillick2026universality,
  title = {{A universality result for the critical 2d stochastic heat flow}},
  author = {Hindy Drillick and Jonathan Hou and Shalin Parekh},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15832},
  eprint = {2609.15832},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15832},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A universality result for the critical 2d stochastic heat flow
AU  - Hindy Drillick
AU  - Jonathan Hou
AU  - Shalin Parekh
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15832
UR  - https://arxiv.org/abs/2609.15832
AB  - For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical 2d stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The class of discrete models we consider includes random walks in space-time random environments with finite-range jumps, and directed polymer models with finite-range spatial correlations. The class of continuum models we consider includes several distinct types of linear-multiplicative stochastic PDEs whose driving noise is Gaussian with a smooth and compactly supported covariance kernel.
ER  -