Universality of deterministic KPZ
arXiv:2102.13131
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.
62 pages. Minor edits and improvements in this revision
References in corpus (7)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Asymptotics in ASEP with Step Initial Condition
- The one-dimensional KPZ equation and its universality class
- A Fredholm Determinant Representation in ASEP
- Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions
- Convergence of deterministic growth models
- Hairer-Quastel universality in non-stationarity via energy solution theory