Maximum of an Airy process plus Brownian motion and memory in KPZ growth
arXiv:1709.06264 · doi:10.1103/PhysRevE.96.060101
Abstract
We obtain several exact results for universal distributions involving the maximum of the Airy process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality class. This allows to obtain (i) the universal limit, for large time separation, of the two-time height correlation for droplet initial conditions, e.g. , with , as well as conditional moments, which quantify ergodicity breaking in the time evolution; (ii) in the same limit, the distribution of the midpoint position of a directed polymer of length , and (iii) the height distribution in stationary KPZ with a step. These results are derived from the replica Bethe ansatz for the KPZ continuum equation, with a "decoupling assumption" in the large time limit. They agree and confirm, whenever they can be compared, with (i) our recent tail results for two-time KPZ with de Nardis, checked in experiments with Takeuchi, (ii) a recent result of Maes and Thiery on midpoint position.
arXiv comment45 pages, 3 figures
References in corpus (41)
- Level-Spacing Distributions and the Airy Kernel
- Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
- Discrete polynuclear growth and determinantal processes
- Free-energy distribution of the directed polymer at high temperature
- Exact scaling functions for one-dimensional stationary KPZ growth
- Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
- A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
- An exact solution for the KPZ equation with flat initial conditions
- A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
- Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
- Full counting statistics in a propagating quantum front and random matrix spectra
- Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
- Exact solution for the stationary Kardar-Parisi-Zhang equation
- Inhomogeneous field theory inside the arctic circle
- Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
- The KPZ equation with flat initial condition and the directed polymer with one free end
- Exact distribution of the maximal height of p vicious walkers
- Stationary correlations for the 1D KPZ equation
- Renormalization fixed point of the KPZ universality class
- Airy processes and variational problems
- Limit process of stationary TASEP near the characteristic line
- Nonintersecting Brownian excursions
- The One-dimensional KPZ Equation and the Airy Process
- Reunion probability of N vicious walkers: typical and large fluctuations for large N
- Memory and universality in interface growth
- Maximum distributions of bridges of noncolliding Brownian paths
- On Time Correlations for KPZ Growth in One Dimension
- Two-point free energy distribution function in (1+1) directed polymers
- Two time distribution in Brownian directed percolation
- Two-time free energy distribution function in (1+1) directed polymers
- Attempted Bethe ansatz solution for one-dimensional directed polymers in random media
- Two-point generating function of the free energy for a directed polymer in a random medium
- On the equal time two-point distribution of the one-dimensional KPZ equation by replica
- Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
- Periodic Airy process and equilibrium dynamics of edge fermions in a trap
- Tail of the two-time height distribution for KPZ growth in one dimension
- Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditions
- On two-time distribution functions in (1+1) random directed polymers
- Crossover between various initial conditions in KPZ growth: flat to stationary
- Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potential
- Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
Cited by in corpus (7)
- Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
- Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
- When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class
- Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica
- Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian case
- The Long ans Short Time Asymptotics of the Two-Time Distribution in Local Random Growth
- KPZ fluctuations in finite volume