# Convergence of deterministic growth models

@inproceedings{Chatterjee2021ConvergenceOD, title={Convergence of deterministic growth models}, author={Sourav Chatterjee and Panagiotis E. Souganidis}, year={2021} }

We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are unique viscosity solutions of firstor second-order partial differential equations depending on whether the growth models are scaled hyperbolically or parabolically. The results simplify and extend a recent work by the first author to more general surface growth models. The proofs are based on…

## 4 Citations

Comparison Principles for Second Order Elliptic/Parabolic Equations with Discontinuities in the Gradient Compatible with Finsler Norms

- Mathematics
- 2021

This paper is about elliptic and parabolic partial differential operators with discontinuities in the gradient which are compatible with a Finsler norm in a sense to be made precise. Examples of this…

Local KPZ behavior under arbitrary scaling limits

- Mathematics
- 2021

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar–Parisi–Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a…

Existence of stationary ballistic deposition on the infinite lattice

- Mathematics
- 2021

A BSTRACT . Ballistic deposition is one of the many models of interface growth that are believed to be in the KPZ universality class, but have so far proved to be largely intractable mathematically.…

Superconcentration in surface growth

- Physics
- 2021

Height functions of growing random surfaces are often conjectured to be superconcentrated, meaning that their variances grow sublinearly in time. This article introduces a new concept — called…

## References

SHOWING 1-10 OF 20 REFERENCES

Comparison Principles for Second Order Elliptic/Parabolic Equations with Discontinuities in the Gradient Compatible with Finsler Norms

- Mathematics
- 2021

This paper is about elliptic and parabolic partial differential operators with discontinuities in the gradient which are compatible with a Finsler norm in a sense to be made precise. Examples of this…

Convergence of approximation schemes for fully nonlinear second order equations

- Mathematics29th IEEE Conference on Decision and Control
- 1990

The convergence of a wide class of approximation schemes to the viscosity solution of fully nonlinear second-order elliptic or parabolic, possibly degenerate, partial differential equations is…

User’s guide to viscosity solutions of second order partial differential equations

- Mathematics
- 1992

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence…

Motion of level sets by mean curvature. I

- Mathematics
- 1991

We continue our investigation of the “level-set” technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature. The principal assertion of this paper is…

Local KPZ behavior under arbitrary scaling limits

- Mathematics
- 2021

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar–Parisi–Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a…

Dynamic scaling of growing interfaces.

- PhysicsPhysical review letters
- 1986

A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.

Some relations between nonexpansive and order preserving mappings

- Mathematics
- 1980

Abstract : It is shown that nonlinear operators which preserve the integral are order preserving if and only if they are nonexpansive in L(1) and that those wich commute with translation by a…

Random Surfaces

- Mathematics
- 2003

We study the statistical physical properties of (discretized) “random surfaces,” which are random functions from Z (or large subsets of Z) to E, where E is Z or R. Their laws are determined by…

Gradient Gibbs measures for the SOS model with countable values on a Cayley tree

- MathematicsElectronic Journal of Probability
- 2019

We consider an SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree of order k and are interested in translation-invariant gradient Gibbs measures (GGMs) of the…

Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

- Mathematics
- 1989

where Vu is the (spatial) gradiant of u. Here VM/|VW| is a unit normal to a level surface of u, so div(Vw/|Vw|) is its mean curvature unless Vu vanishes on the surface. Since ut/\Vu\ is a normal…