Universality of deterministic KPZ
Probability
2021-09-07 v4 Statistical Mechanics
Mathematical Physics
Analysis of PDEs
math.MP
Abstract
Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone, invariant under the symmetries of the lattice, equivariant under constant shifts, and twice continuously differentiable, it is shown that any such growing surface approaches a solution of the deterministic KPZ equation in a suitable space-time scaling limit.
Cite
@article{arxiv.2102.13131,
title = {Universality of deterministic KPZ},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:2102.13131},
year = {2021}
}
Comments
62 pages. Minor edits and improvements in this revision