相关论文: Sharp moment and upper tail asymptotics for the cr…
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…
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) 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 Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE), specifically at the critical dimension of two and near the critical temperature.…
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 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…
We determine a $q\to 1$ limit of the two-dimensional $q$-Whittaker driven particle system on the torus studied previously in [Corwin-Toninelli, arXiv:1509.01605]. This has an interpretation as a $(2+1)$-dimensional stochastic interface…
Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…
The partition function of the directed polymer model on Z^{2+1} undergoes a phase transition in a suitable continuum and weak disorder limit. In this paper, we focus on a window around the critical point. Exploiting local renewal theorems,…
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…
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth, random deposition... Interesting limits arise at large…
We study the critical two-dimensional stochastic heat flow $\mathscr{Z}_t^{\vartheta}$, recently constructed as the scaling limit of directed polymers in a random environment and as the weak limit of the solution to a mollified stochastic…
The $(d+1)$-dimensional KPZ equation is the canonical model for the growth of rough $d$-dimensional random surfaces. A deep mathematical understanding of the KPZ equation for $d=1$ has been achieved in recent years, and the case $d\ge 3$…
In this article, we consider the $d$-dimensional mollified stochastic heat equation (SHE) when the mollification parameter is turned off. Here, we concentrate on the high-dimensional case $d \geq 3$. Recently, the limiting higher moments of…
We extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that…
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…
We consider a directed polymer model in dimension $1+1$, where the disorder is given by the occupation field of a Poisson system of independent random walks on $\mathbb Z$. In a suitable continuum and weak disorder limit, we show that the…
The exponential-tail behaviours of the probability density function (PDF) of the primordial curvature perturbation are confirmed in the mild-waterfall variants of hybrid inflation with the use of the stochastic formalism of inflation. On…