The 1 + 1-dimensional Kardar–Parisi–Zhang equation and its universality class
From MaRDI portal
Publication:3301137
DOI10.1088/1742-5468/2010/11/P11013zbMath1459.82195arXiv1010.2691OpenAlexW2060089654MaRDI QIDQ3301137
Tomohiro Sasamoto, Herbert Spohn
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/1010.2691
Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) PDEs in connection with statistical mechanics (35Q82)
Related Items (31)
Determinantal structures in the O'Connell-Yor directed random polymer model ⋮ Exact lower-tail large deviations of the KPZ equation ⋮ KPZ line ensemble ⋮ KPZ and Airy limits of Hall-Littlewood random plane partitions ⋮ Limiting current distribution for a two species asymmetric exclusion process ⋮ Stationary solutions to the stochastic Burgers equation on the line ⋮ Lower tail of the KPZ equation ⋮ Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process ⋮ Fluctuation exponents of the KPZ equation on a large torus ⋮ Perturbative solution for the spectral gap of the weakly asymmetric exclusion process ⋮ Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation ⋮ New approach to KPZ models through free fermions at positive temperature ⋮ Crossover to the KPZ equation ⋮ A multi-layer extension of the stochastic heat equation ⋮ Tracy-Widom distributions for the Gaussian orthogonal and symplectic ensembles revisited: a skew-orthogonal polynomials approach ⋮ The periodic Schur process and free fermions at finite temperature ⋮ Two-point generating function of the free energy for a directed polymer in a random medium ⋮ The one-dimensional KPZ equation and the Airy process ⋮ Experimental approaches to universal out-of-equilibrium scaling laws: turbulent liquid crystal and other developments ⋮ Boundary crossover in semi-infinite non-equilibrium growth processes ⋮ Current fluctuations and large deviations for periodic TASEP on the relaxation scale ⋮ Hyperskewness of (1 + 1)-dimensional KPZ height fluctuations ⋮ On global solutions of the random Hamilton–Jacobi equations and the KPZ problem ⋮ The lower tail of the half-space KPZ equation ⋮ Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes ⋮ Observables of Macdonald processes ⋮ Fractional moments of the stochastic heat equation ⋮ Nonstationary generalized TASEP in KPZ and jamming regimes ⋮ The intermediate disorder regime for Brownian directed polymers in Poisson environment ⋮ On asymmetric simple exclusion process with periodic step Bernoulli initial condition ⋮ Height fluctuations for the stationary KPZ equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Exact height distributions for the KPZ equation with narrow wedge initial condition
- New bounds for the free energy of directed polymers in dimension \(1+1\) and \(1+2\)
- Integral formulas for the asymmetric simple exclusion process
- A Fredholm determinant representation in ASEP
- Asymptotics in ASEP with step initial condition
- Level-spacing distributions and the Airy kernel
- Stochastic Burgers and KPZ equations from particle systems
- Limiting distributions for a polynuclear growth model with external sources
- A condition for weak disorder for directed polymers in random environment
- Shape fluctuations and random matrices
- Fluctuation properties of the TASEP with periodic initial configuration
- A pedestrian's view on interacting particle systems, KPZ universality and random matrices
- Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
- Bethe ansatz solution for one-dimensional directed polymers in random media
- Dynamic Scaling of Growing Interfaces
- Directed polymers in a random medium: 1/d expansion and the n-tree approximation
- Transition between Airy1and Airy2processes and TASEP fluctuations
- On the numerical evaluation of Fredholm determinants
- Moment Problem in Replica Method
- An Introduction to Random Matrices
- On the distribution of the length of the longest increasing subsequence of random permutations
- Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
- Statistical Physics of Fields
- The crossover regime for the weakly asymmetric simple exclusion process
This page was built for publication: The 1 + 1-dimensional Kardar–Parisi–Zhang equation and its universality class
