The one-dimensional KPZ equation and the Airy process

DOI10.1088/1742-5468/2011/03/P03020zbMath1456.82711arXiv1101.4622OpenAlexW1973118293MaRDI QIDQ3301239

Sylvain Prolhac, 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/1101.4622

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Brownian motion (60J65) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Exactly solvable dynamic models in time-dependent statistical mechanics (82C23)

Related Items (15)

Airy Processes and Variational Problems ⋮ Midpoint distribution of directed polymers in the stationary regime: exact result through linear response ⋮ Local behavior and hitting probabilities of the \(\text{Airy}_1\) process ⋮ Directed random polymers via nested contour integrals ⋮ Delta-Bose gas on a half-line and the Kardar–Parisi–Zhang equation: boundary bound states and unbinding transitions ⋮ Bethe ansatz replica derivation of the GOE Tracy–Widom distribution in one-dimensional directed polymers with free endpoints ⋮ The KPZ equation with flat initial condition and the directed polymer with one free end ⋮ Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz ⋮ Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz ⋮ Two-time distribution functions in the Gaussian model of randomly forced Burgers turbulence ⋮ Crossover between various initial conditions in KPZ growth: flat to stationary ⋮ Tail of the two-time height distribution for KPZ growth in one dimension ⋮ Log-gamma directed polymer with one free end via coordinate Bethe Ansatz ⋮ Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles ⋮ Tracy-Widom distribution, Airy\(_2\) process and its sample path properties

Cites Work

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• Exact height distributions for the KPZ equation with narrow wedge initial condition
• Norms of bound states
• Scale invariance of the PNG droplet and the Airy process
• The arctic circle boundary and the Airy process
• Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
• The 1 + 1-dimensional Kardar–Parisi–Zhang equation and its universality class
• Two-point generating function of the free energy for a directed polymer in a random medium
• Dynamic Scaling of Growing Interfaces
• Dynamics of the attractive 1D Bose gas: analytical treatment from integrability
• The crossover regime for the weakly asymmetric simple exclusion process

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