## 4 Citations

### Effective upper bound of analytic torsion under Arakelov metric.

- Mathematics
- 2019

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

- Mathematics, Computer Science
- 2022

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

- Mathematics
- 2019

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

- MathematicsJournal of Statistical Physics
- 2019

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…

## References

SHOWING 1-10 OF 30 REFERENCES

### Gaussian free fields for mathematicians

- Mathematics
- 2003

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

- MathematicsStochastic Processes and their Applications
- 2019

### Extrema of the Two-Dimensional Discrete Gaussian Free Field

- MathematicsSpringer 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

- Mathematics
- 2017

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…

### A universal bound on the gradient of logarithm of the heat kernel for manifolds with bounded Ricci curvature

- Mathematics
- 2006

### Towards a theoretical foundation for Laplacian-based manifold methods

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2008

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

- Computer Science, MathematicsCOLT
- 2005

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

- Mathematics
- 2012

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

- MathematicsThe Annals of Probability
- 2019

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

- Mathematics, Physics
- 2014

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…