Brownian bridge limit of path measures in the upper tail of KPZ models
For models in the KPZ universality class, such as the zero temperature model of planar last
passage-percolation (LPP) and the positive temperature model of directed polymers, its …
passage-percolation (LPP) and the positive temperature model of directed polymers, its …
Jointly invariant measures for the Kardar-Parisi-Zhang equation
We give an explicit description of the jointly invariant measures for the KPZ equation. These
are couplings of Brownian motions with drift, and can be extended to a process defined for …
are couplings of Brownian motions with drift, and can be extended to a process defined for …
Characterization of the directed landscape from the KPZ fixed point
D Dauvergne, L Zhang - arxiv preprint arxiv:2412.13032, 2024 - arxiv.org
We show that the directed landscape is the unique coupling of the KPZ fixed point from all
initial conditions at all times satisfying three natural properties: independent increments …
initial conditions at all times satisfying three natural properties: independent increments …
Fluctuation exponents of the half-space KPZ at stationarity
We study the half-space KPZ equation with a Neumann boundary condition, starting from
stationary Brownian initial data. We derive a variance identity that links the fluctuations of the …
stationary Brownian initial data. We derive a variance identity that links the fluctuations of the …
Viscous shock fluctuations in KPZ
We study``V-shaped''solutions to the KPZ equation, those having opposite asymptotic slopes
$\theta $ and $-\theta $, with $\theta> 0$, at positive and negative infinity, respectively …
$\theta $ and $-\theta $, with $\theta> 0$, at positive and negative infinity, respectively …