We establish the first tight bound on lower tail probability of half-space KPZ equation with Neumann boundary parameter A=−1/2 and narrow-wedge initial data. The demonstrates a crossover between two regimes super-exponential decay exponents 52 3; upper 32 3. Given crude leading-order asymptotic in Stokes region for Ablowitz–Segur solution to Painlevé II (Definition 1.8), we improve demonstrate ...

The Kardar–Parisi-Zhang (KPZ) equation is examined using the recently published leapfrog–hopscotch (LH) method as well most standard forward time centered space (FTCS) scheme and Heun method. methods are verified by reproducing an analytical solution. performance of each then compared calculating average maximum differences among results displaying runtimes. Numerical tests show that due to spe...

Consider the Hopf–Cole solution h(t,x) of Kandar–Parisi–Zhang (KPZ) equation with narrow wedge initial condition. Regarding t→∞ as a scaling parameter, we provide first rigorous proof large deviation principle (LDP) for lower tail h(2t,0)+t 12, speed t2 and an explicit rate function Φ −(z). This result confirms existing physics predictions made by Corwin (2011); Sasorov, Meerson, Prolhac (2017)...

A Correction to this paper has been published: https://doi.org/10.1007/s11040-021-09380-8

The statistics of the average height fluctuation of the one-dimensional 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 ≪ N with t time and N the system size, from the known characteristic function in the stationary state (t ≫ N) of the single-step model derivab...

Thanks to a fluctuation dissipation theorem and the mapping to exactly solvable models, much is known for space-dimension d = 1 [1, 2, 3]. In contrast, the case of d ≥ 2 can only be attacked by approximative methods or field-theoretic perturbative expansions. Using the latter, the fixed point structure of the renormalization group flow for d = 2 + ε has been obtained [1, 4, 5]. Two domains can ...

Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); see e.g. [3, 5, 9, 16, 21, 22, 25, 26]. The situation is quite different for what concerns stochastic differential equations [1, 13, 14, 17, 20]: here, symmetry considerations are of course quite widely used by theoretical physicists (see e.g. [4, 15, 18] in the c...