Related papers: Universality of deterministic KPZ
We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface,…
We report on the first exact solution of the KPZ equation in one dimension, with an initial condition which physically corresponds to the motion of a macroscopically curved height profile. The solution provides a determinantal formula for…
There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting…
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original…
We classify entire 2-dimensional area-minimizing or stable surfaces in R^4 with quadratic area growth as algebraic, cut out by a finite union of holomorphic polynomials whose collective degrees are controlled by the density at infinity. As…
We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschitz continuous, they grow as a linear function, are strongly…
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L}…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
The main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local "gradient terms". More precisely, let $\Omega \subset \mathbb{R}^N$, $N \geq 2$, be a…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…
A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a…
Analysis of non-compact manifolds almost always requires some controlled behavior at infinity. Without such, one neither can show, nor expect, strong properties. On the other hand, such assumptions restrict the possible applications and…
In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of…
We announce the folowing result: Any finitely generated non virtually solvable linear group over a field of characteristic zero has uniform exponential growth.
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with…
We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the…
We propose Josephson junction arrays as realistic platforms for observing nonequilibrium scaling laws characterizing the Kardar-Parisi-Zhang (KPZ) universality class, and space-time soliton proliferation. Focusing on a two-chain ladder…