相关论文: Properties of the gradient squared of the discrete…

We consider nonlinear functionals of discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of $\mathbb{Z}^{2}$, including i.i.d. supercritical percolation clusters, where the conductances are possibly…

Consider a doubly-infinite array of iid centered variables with moment conditions, from which one can extract a finite number of rectangular, overlapping submatrices, and form the corresponding Wishart matrices. We show that under basic…

We study the scaling limit of statistical mechanics models with non-convex Hamiltonians that are gradient perturbations of Gaussian measures. Characterising features of our gradient models are the imposed boundary tilt and the surface…

The d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are…

We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to…

We study the discrete massless Gaussian Free Field on Z^d, d \geq 2, in the presence of a disordered square-well potential supported on a finite strip around zero. The disorder is introduced by reward/penalty interaction coefficients, which…

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…

In this paper, we study a natural discretization of the smooth Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of a geodesic disk at a vertex of a polyhedral surface. It is proved that each…

We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…

We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in…

We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the way we obtain the discrete analogue of the classical…

We consider the dimer model in cylindrical domains $\Omega_\delta$ on square grids of mesh size $\delta$ with two Temperleyan boundary components of different colors. Assuming that the $\Omega_\delta$ approximate a cylindrical domain…

Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of…

We prove convergence of the full extremal process of the two-dimensional scale-inhomogeneous discrete Gaussian free field in the weak correlation regime. The scale-inhomogeneous discrete Gaussian free field is obtained from the 2d discrete…

We investigate the percolation phase transition for level sets of the Gaussian free field on $\mathbb{Z}^d$, with $d\geqslant 3$, and prove that the corresponding critical parameter $h_*(d)$ is strictly positive for all $d\geqslant3$, thus…

The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that its macroscopic scaling limit on the torus is a multiple of the Gaussian free…

We show that the rescaled maximum of the discrete Gaussian Free Field (DGFF) in dimension larger or equal to 3 is in the maximal domain of attraction of the Gumbel distribution. The result holds both for the infinite-volume field as well as…

We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…

In this paper we investigate the height field of a dimer model/random domino tiling on the plane at a smooth-rough (i.e. gas-liquid) transition. We prove that the height field at this transition has two-point correlation functions which…

The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is…