相关论文: Conditional GMC within the stochastic heat flow
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…
We consider a {\it{Gaussian multiplicative chaos}} (GMC) measure on the classical Wiener space driven by a smoothened (Gaussian) space-time white noise. For $d\geq 3$ it was shown in \cite{MSZ16} that for small noise intensity, the total…
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.…
In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means…
Gaussian multiplicative chaos (GMC) is a canonical random fractal measure obtained by exponentiating log-correlated Gaussian processes, first constructed in the seminal work of Kahane (1985). Since then it has served as an important…
In this article, we consider the multiplicative chaos measure associated to the log-correlated random Fourier series, or random wave model, with i.i.d. coefficients taken from a general class of distributions. This measure was shown to be…
The complex Gaussian Multiplicative Chaos (or complex GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is a log correlated Gaussian field on $\mathbb R^d$ and $\gamma=\alpha+i\beta$ is a complex…
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 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…
Gaussian Multiplicative Chaos (GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is Gaussian field on $\mathbb R^d$ (or an open subset of it) whose correlation function is of the form $ K(x,y)= \log…
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 purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet boundary condition but with a nontrivial…
We construct and study properties of an infinite dimensional analog of Kahane's theory of Gaussian multiplicative chaos \cite{K85}. Namely, if $H_T(\omega)$ is a random field defined w.r.t. space-time white noise $\dot B$ and integrated…
We develop an approach for investigating geometric properties of Gaussian multiplicative chaos (GMC) in an infinite dimensional set up. The base space is chosen to be the space of continuous functions endowed with Wiener measure, and the…
We provide new constructions of the subcritical and critical Gaussian multiplicative chaos (GMC) measures corresponding to the 2D Gaussian free field (GFF). As a special case we recover E. Aidekon's construction of random measures using…
The present article concerns the stochastic modeling of the turbulent dissipation field and in particular its temporal evolution. To do so, we will be calling for a random distribution, ubiquitous in several aspects of physics and…
The objective of this note is to study the probability that the total mass of a sub-critical Gaussian multiplicative chaos (GMC) with arbitrary base measure $\sigma$ is small. When $\sigma$ has some continuous density w.r.t Lebesgue…
We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which…
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…
We introduce and study the flow of metrics on a foliated Riemannian manifold $(M,g)$, whose velocity along the orthogonal distribution is proportional to the mixed scalar curvature, $\Sc_{\,\rm mix}$. The flow is used to examine the…