The discrete Gaussian free field on a compact manifold

  title={The discrete Gaussian free field on a compact manifold},
  author={Alessandra Cipriani and Bart van Ginkel},
  journal={Stochastic Processes and their Applications},

Effective upper bound of analytic torsion under Arakelov metric.

Given a choice of metric on the Riemann surface, the regularized determinant of Laplacian (analytic torsion) is defined via the complex power of elliptic operators: $$ \det(\Delta)=\exp(-\zeta'(0))

Dirichlet fractional Gaussian fields on the Sierpinski gasket and their discrete graph approximations

The Dirichlet fractional Gaussian fields on the Sierpinski gasket are defined and studied and it is shown that they are limits of fractional discreteGaussian fields defined on the sequence of canonical approximating graphs.

Odometers of Divisible Sandpile Models: Scaling Limits, iDLA and Obstacle Problems. A Survey

The divisible sandpile model is a fixed-energy continuous counterpart of the Abelian sandpile model. We start with a random initial configuration and redistribute mass deterministically. Under

Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian



Gaussian free fields for mathematicians

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

Local picture and level-set percolation of the Gaussian free field on a large discrete torus

Extrema of the Two-Dimensional Discrete Gaussian Free Field

  • M. Biskup
  • Mathematics
    Springer Proceedings in Mathematics & Statistics
  • 2019
These lecture notes offer a gentle introduction to the two-dimensional Discrete Gaussian Free Field with particular attention paid to the scaling limits of the level sets at heights proportional to

Invariance principle and hydrodynamic limits on Riemannian manifolds

In this report we study Markov processes on compact and connected Riemannian manifolds. We define a random walk on such manifolds and give a direct proof of the invariance principle. This principle

Towards a theoretical foundation for Laplacian-based manifold methods

From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians

This paper establishes the strong pointwise consistency of a family of graph Laplacians with data-dependent weights to some weighted Laplace operator.

Heat Kernel and Analysis on Manifolds

Laplace operator and the heat equation in $\mathbb{R}^n$ Function spaces in $\mathbb{R}^n$ Laplace operator on a Riemannian manifold Laplace operator and heat equation in $L^{2}(M)$ Weak maximum

The scaling limit of the membrane model

On the integer lattice we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane

Fractional Gaussian fields: A survey

We discuss a family of random fields indexed by a parameter s ∈ R which we call the fractional Gaussian fields, given by FGFs(R) = (−∆)−s/2W, where W is a white noise on Rd and (−∆)−s/2 is the