Related papers: Stochastic heat flow by moments
The Critical $2d$ Stochastic Heat Flow (SHF) is a measure valued stochastic process on $\mathbb{R}^2$ that defines a non-trivial solution to the two-dimensional stochastic heat equation with multiplicative space-time noise. Its one-time…
The critical 2D Stochastic Heat Flow (SHF) is a universal measure-valued process that provides a notion of solution to the ill-defined 2D stochastic heat equation. We investigate the SHF in the large-time and strong-disorder regimes,…
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…
We review our joint work on the scaling limits of disordered systems, linking the notion of disorder relevance/irrelevance to that of sub/super-criticality of singular SPDEs. This line of research culminated in the construction of the…
The critical $2d$ Stochastic Heat Flow (SHF) is a stochastic process of random measures on ${\mathbb R}^2$, recently constructed in [CSZ23]. We show that this process falls outside the class of Gaussian Multiplicative Chaos (GMC), in the…
In [CSZ23], the authors proved the convergence of the finite dimensional time distribution of the rescaled random fields derived from the discrete stochastic heat equation of $2d$-directed polymers in random environment in the critical…
In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was discovered that a phase transition emerges on an…
While $1+1$ dimensional growth models in the Kardar-Parisi-Zhang universality class have witnessed an explosion of activity, higher dimensional models remain much less explored. The special case of $2+1$ dimensions is particularly…
We consider directed polymers in random environment in the critical dimension $d = 2$, focusing on the intermediate disorder regime when the model undergoes a phase transition. We prove that, at criticality, the diffusively rescaled random…
An experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh…
A recent paper of Tsai shows how the first few moments of a stochastic flow in the space of measures can completely determine its law. Here we give another proof of this result for the particular case of the one-dimensional multiplicative…
We establish that the family of polymer measures $M^{\theta}_{[s,t]}$ associated with the Stochastic Heat Flow (SHF), indexed by $\theta\in\mathbb{R}$, has a conditional Gaussian Multiplicative Chaos (GMC) structure. Namely, taking the…
When modelling phase change, the latent heat released (absorbed) during solidification (melting) must be included in the heat transfer equation. In this paper, different SPH methods for the implementation of latent heat, in the context of…
We define linear stochastic heat equations (SHE) on p.c.f.s.s. sets equipped with regular harmonic structures. We show that if the spectral dimension of the set is less than two, then function-valued "random-field" solutions to these SPDEs…
We study the stochastic heat flow with constant initial data and analyze its spatial average on the scale of $\varepsilon\ll1$. We prove that the logarithm of the averaged process satisfies a pointwise central limit theorem: After being…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
A non-equilibrium steady state thermodynamics to describe shear flows is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian…
We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random walk whose transition probabilities are iid [0,1]-valued…
Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition. Recently, SHD has been observed in confined…
In this contribution, we provide convergence rates for a finite volume scheme of the stochastic heat equation with multiplicative Lipschitz noise and homogeneous Neumann boundary conditions (SHE). More precisely, we give an error estimate…