# Short-time height distribution in 1d KPZ equation: starting from a parabola

@inproceedings{Kamenev2016ShorttimeHD, title={Short-time height distribution in 1d KPZ equation: starting from a parabola}, author={Alex Kamenev and Baruch Meerson and Pavel Sasorov}, year={2016} }

We study the probability distribution P(H, t, L) of the surface height h(x = 0, t) = H in the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimension when starting from a parabolic interface, h(x, t = 0) = x/L. The limits of L → ∞ and L → 0 have been recently solved exactly for any t > 0. Here we address the early-time behavior of P(H, t, L) for general L. We employ the weak-noise theory a variant of WKB approximation – which yields the optimal history of the interface, conditioned on reaching…

## 9 Citations

### Large fluctuations of the KPZ equation in a half-space

- MathematicsSciPost Physics
- 2018

We investigate the short-time regime of the KPZ equation in
1+11+1
dimensions and develop a unifying method to obtain the height
distribution in this regime, valid whenever an exact solution exists…

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We study the long-time regime of the Kardar–Parisi–Zhang (KPZ) equation in 1 + 1 dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large…

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### Large deviations for the Kardar– Parisi–Zhang equation from the Kadomtsev–Petviashvili equation

- Mathematics
- 2020

Recently, Quastel and Remenik (2019 (arXiv:1908.10353)) found a remarkable relation between some solutions of the finite time Kardar–Parisi–Zhang (KPZ) equation and the Kadomtsev–Petviashvili (KP)…

### Large deviations for the KPZ equation from the KP equation

- Mathematics
- 2019

Recently, Quastel and Remenik \cite{QRKP} [arXiv:1908.10353] found a remarkable relation between some solutions of the finite time Kardar-Parisi-Zhang (KPZ) equation and the Kadomtsev-Petviashvili…

### Inverse Scattering of the Zakharov-Shabat System Solves the Weak Noise Theory of the Kardar-Parisi-Zhang Equation.

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The program of the weak noise theory is expanded, which maps the large deviations onto a nonlinear hydrodynamic problem, and its complete solvability is unveiled through a connection to the integrability of the Zakharov-Shabat system.

### Short Time Large Deviations of the KPZ Equation

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- 2021

We establish the Freidlin–Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a small parameter…

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- Physics, Mathematics
- 2019

Cette these de doctorat porte sur l'etude du modele de croissance stochastique Kardar-Parisi-Zhang (KPZ) en 1+1 dimensions et en particulier de l'equation qui le regit. Cette these est d'une part…

### Probing large deviations of the Kardar-Parisi-Zhang equation at short times with an importance sampling of directed polymers in random media.

- PhysicsPhysical review. E
- 2020

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature, showing spectacular agreement with the analytical expressions.

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