REVIEW 7 cited by
Singularity and regularity of the critical 2D Stochastic Heat Flow
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
The Critical 2D Stochastic Heat Flow (SHF) provides a natural candidate solution to the ill-posed 2D Stochastic Heat Equation with multiplicative space-time white noise. In this paper, we initiate the investigation of the spatial properties of the SHF. We prove that, as a random measure on $\mathbb{R}^2$, it is a.s. singular w.r.t. the Lebesgue measure. This is obtained by probing a "quasi-critical" regime and showing the asymptotic log-normality of the mass assigned to vanishing balls, as the disorder strength is sent to zero at a suitable rate, accompanied by similar results for critical 2D directed polymers. We also describe the regularity of the SHF, showing that it is a.s. H\"older $C^{-\epsilon}$ for any $\epsilon>0$, implying the absence of atoms, and we establish local convergence to zero in the long time limit.
Forward citations
Cited by 7 Pith papers
-
Logarithmic intermittency of the critical 2D SHF
For the critical 2D stochastic heat flow, the minimal number of ε-balls carrying almost all mass is ε^{-2}(log 1/ε)^{-1/2+o(1)}, with the complementary sparsity bound holding simultaneously.
-
The critical KPZ scale for the Averaging Process
The averaging process has KPZ critical scale λ=7/8 rather than the moment-criterion value 3/4, with tilted fields converging to the multiplicative SHE of noise 1/√2.
-
Sharp moment and upper tail asymptotics for the critical $2d$ Stochastic Heat Flow
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.
-
Conditional GMC within the stochastic heat flow
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).
-
Extrema of cooling branching Brownian motion and related Gaussian fields
Introduces slowed-down Gaussian fields (including 1D branching Brownian motions in cooling environments) and proves tightness of maxima with growth T^{1-α} and phase transition at α=1/3.
-
Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow
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.
-
Stochastic heat flow is a black noise
The stochastic heat flow is a black noise, meaning its linear random-variable space is trivial, and consequently the critical 2d SHE is asymptotically independent of its mollified driving noise.
Discussion (0). Continue with ORCID to comment.