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Continuum polymer measures corresponding to the critical 2d stochastic heat flow

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arxiv 2409.01510 v1 pith:7TTYGAYL submitted 2024-09-03 math.PR

Jeremy Clark , Barkat Mian This is my paper · ORCID
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sharp moment and upper tail asymptotics for the critical $2d$ Stochastic Heat Flow

    math.PR 2025-07 conditional novelty 8.0 of 10

    The h-th moment of the critical 2d Stochastic Heat Flow mass is at least exp(exp(c h)), matching a 1999 prediction and exponentially improving the known lower bound.

  2. Conditional GMC within the stochastic heat flow

    math.PR 2025-07 conditional novelty 8.0 of 10

    The family of polymer measures of the critical 2D stochastic heat flow has a conditional GMC structure: a GMC with noise strength a maps M^theta in law to M^(theta+a).

  3. Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow

    math.PR 2025-07 conditional novelty 7.0 of 10

    A general, rate-optimal BKS noise-sensitivity criterion is proven, and it yields the independence of the critical 2D Stochastic Heat Flow from the disorder white noise.

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