Large deviations of surface height in the 1 + 1-dimensional Kardar–Parisi–Zhang equation: exact long-time results for λH<0

DOI10.1088/1742-5468/aa73f8zbMath1457.82301arXiv1703.03310OpenAlexW2610215626MaRDI QIDQ3303084

Baruch Meerson, Sylvain Prolhac, Pavel V. Sasorov

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.03310

Mathematics Subject Classification ID

PDEs with randomness, stochastic partial differential equations (35R60) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)

Related Items (24)

Large deviations of the KPZ equation via the stochastic Airy operator ⋮ Noninteracting fermions in a trap and random matrix theory ⋮ Geometrical optics of constrained Brownian motion: three short stories ⋮ Exact lower-tail large deviations of the KPZ equation ⋮ Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ ⋮ Lower tail of the KPZ equation ⋮ Integrability in the weak noise theory ⋮ KPZ equation with a small noise, deep upper tail and limit shape ⋮ Dynamics of fluctuations in the Gaussian model with conserved dynamics ⋮ Large deviations for the Kardar– Parisi–Zhang equation from the Kadomtsev–Petviashvili equation ⋮ Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions ⋮ The lower tail of the half-space KPZ equation ⋮ Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermions ⋮ Extreme statistics and index distribution in the classical 1dCoulomb gas ⋮ Lyapunov exponents of the half-line SHE ⋮ Fractional moments of the stochastic heat equation ⋮ Short time large deviations of the KPZ equation ⋮ Finite-size effects in the short-time height distribution of the Kardar–Parisi–Zhang equation ⋮ Nonequilibrium steady state of a weakly-driven Kardar–Parisi–Zhang equation ⋮ Simple derivation of the (– λ H)^5/2 tail for the 1D KPZ equation ⋮ Airy kernel determinant solutions to the KdV equation and integro-differential Painlevé equations ⋮ Upper-tail large deviation principle for the ASEP ⋮ KPZ equation tails for general initial data ⋮ Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks

Uses Software

• Mathematica
• DLMF

Cites Work

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• Solving the KPZ equation
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• A KPZ cocktail-shaken, not stirred\dots: Toasting 30 years of kinetically roughened surfaces
• Asymptotics of the Airy-kernel determinant
• Level-spacing distributions and the Airy kernel
• Limiting distributions for a polynuclear growth model with external sources
• On orthogonal and symplectic matrix ensembles
• Stationary correlations for the 1D KPZ equation
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Dynamic Scaling of Growing Interfaces
• On the numerical evaluation of Fredholm determinants
• On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review

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