Related papers: Gaussian free fields for mathematicians

Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion…

Consider a Brownian loop soup $\mathcal{L}_D^\theta$ with subcritical intensity $\theta \in (0,1/2]$ in some 2D bounded simply connected domain. We define and study the properties of a conformally invariant field $h_\theta$ naturally…

Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present…

We prove that under the Brownian evolution on large non-Hermitian matrices the log-determinant converges in distribution to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, namely it is logarithmically correlated…

In the Kaluza - Klein approach the (4+d)-dimensional Einstein--Hilbert gravity action is considered. The extra d-dimensional manifold V_d is a Riemann space with the d-parametric group of isometry $G_d$ which acts on V_d by the left shifts…

Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…

Nonintersecting motion of Brownian particles in one dimension is studied. The system is constructed as the diffusion scaling limit of Fisher's vicious random walk. N particles start from the origin at time t=0 and then undergo mutually…

We consider the equilibrium surface of the Random Average Process started from an inclined plane, as seen from the height of the origin, obtained in [Ferrari & Fontes, 1998], where its fluctuations were shown to be of order of the square…

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…

Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close to that of a fractional Brownian motion with…

In this paper we show that using frame-like gauge invariant formulation for the massive bosonic and fermionic fields in three dimensions the free Lagrangians for these fields can be rewritten in the explicitly gauge invariant form in terms…

We consider a two parameter family of unitarily invariant diffusion processes on the general linear group $\mathbb{GL}_N$ of $N\times N$ invertible matrices, that includes the standard Brownian motion as well as the usual unitary Brownian…

This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a space-time Gaussian field W assumed to be white noise in time and function-valued in space. According to…

We show that Euclidean 3D-gravity coupled to a Gaussian scalar massive matter field in first-order dreibein formalism gives a quantum theory which has a finite perturbative expansion around a non-vanishing background. We also discuss a…

Fractional Brownian motion (FBM) is the only Gaussian self-similar process with stationary increments. Its increment process, called fractional Gaussian noise, is ergodic and exhibits a property of power-like decaying autocorrelation…

The manifestly gauge invariant formulation for free symmetric partially massless fields in $(A)dS_d$ is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of $(o(d-1,2)) o(d,1)$…

We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…

We study two dimensional massless field in a box with potential $V\left( \nabla \phi \left( \cdot \right) \right) $ and zero boundary condition, where $V$ is any symmetric and uniformly convex function. Naddaf-Spencer and Miller proved the…

We show that Einstein's main equations for stationary axisymmetric fields in vacuum are equivalent to the motion equations for bosonic strings moving on a special nonflat background. This new representation is based on the analysis of…

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as…