We show that under the 1:2:3 scaling, critically probing large space and time, height function of finite range asymmetric exclusion processes Kardar-Parisi-Zhang (KPZ) equation converge to KPZ fixed point, constructed earlier as a limit totally simple process through exact formulas. Consequently, based on recent results Wu [Tightness local fluctuation estimates for line ensemble</italic...

The statistics of isoheight lines in the (2+1) -dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformally invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of exact analytical results for the KPZ dynamics. We present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called Schramm-Loew...

The statistics of the average height fluctuation of the onedimensional Kardar–Parisi–Zhang (KPZ)-type surface is investigated. Guided by the idea of local stationarity, we derive the scaling form of the characteristic function in the early-time regime, t N3/2 with t time and N the system size, from the known characteristic function in the stationary state (t N3/2) of the single-step model deriv...

We prove an extension of a seminal result Bertini and Giacomin. Namely we consider weakly asymmetric exclusion processes with several distinct initial data simultaneously. run their dynamics according to basic coupling, show joint convergence the solution KPZ equation same driving noise in limiting equation. Along way, analyze fine properties nontrivially coupled solutions-in-law KPZ-type equat...