Abstract In this paper we study the Kardar–Parisi–Zhang (KPZ) line ensemble under KPZ scaling. Based on their Gibbs property, derive quantitative local fluctuation estimates for scaled ensemble. This allows us to show tightness of Together with recent progress in [33], [36], and [15], result yields conjectural convergence Airy

This article studies the inhomogeneous geometric polynuclear growth model; distribution of which is related to Schur functions. We explain a method derive its functions in both space-like and time-like directions, focusing on two-time distribution. Asymptotics KPZ-scaling limit then considered, extending two times several single-time distributions KPZ universality class.

The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic potential due to the discrete size of the particles (or to the lattice structure of the crystal) as well as the term introduced by Kardar, Parisi, and Zhang (KPZ) t...

Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π)−1 ∫ D ∇h(z) · ∇h(z)dz, and a constant 0 ≤ γ < 2. The Liouville quantum gravity measure on D is the weak limit as ε → 0 of the measures ε 2/2eγhε(z)dz, where dz is Lebesgue measure on D and hε(z) denotes the mean value of h on the circle of radius ε centered at z. Given a random (or dete...

This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by exploiting an underlying quantum gravity (QG) structure, which uses KPZ maps relating exponents in the plane to those on a random lattice, i.e., in a fluctuating met...

In the present work we study existence and non-existence of nonnegative solutions to a class deterministic KPZ system with nonlocal gradient term. More precisely will consider system$ \begin{equation*} \left\{ \begin{array}{rcll} (-\Delta)^{s} u &amp; = &amp;|\mathbb{D}_{s} v|^q + \rho f\,, \quad {\rm{in }}\; \Omega,\\ v |\mathbb{D}_{s} u|^p \tau g\,, v&amp; 0 &amp;\quad {\text{in }} \mathbb{R}...

The flux of cells at the cell colony border region is expected to be controlled by ridge-patterned substrates, and displacement velocity influenced orientation ridges with respect contour. In this work patterns regularly separated are employed fabricate tilted initially quasi-linear fronts different tilt angles s. For periods in 3.3 – 5.2 µm range, morphological characteristics pattern, individ...

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ...