# Half-space stationary Kardar–Parisi–Zhang equation beyond the Brownian case

@article{Barraquand2022HalfspaceSK, title={Half-space stationary Kardar–Parisi–Zhang equation beyond the Brownian case}, author={Guillaume Barraquand and Alexandre Krajenbrink and Pierre Le Doussal}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

We study the Kardar–Parisi–Zhang (KPZ) equation on the half-line x ⩾ 0 with Neumann type boundary condition. Stationary measures of the KPZ dynamics were characterized in recent work: they depend on two parameters, the boundary parameter u of the dynamics, and the drift −v of the initial condition at infinity. We consider the fluctuations of the height field when the initial condition is given by one of these stationary processes. At large time t, it is natural to rescale parameters as (u, v…

## 4 Citations

### Stationary measures for the log-gamma polymer and KPZ equation in half-space

- Mathematics
- 2022

. We construct explicit one-parameter families of stationary measures for the Kardar-Parisi-Zhang equation in half-space with Neumann boundary conditions at the origin, as well as for the log-gamma…

### On the exponent governing the correlation decay of the Airy$_1$ process

- Mathematics
- 2022

We study the decay of the covariance of the Airy1 process, A1, a stationary stochastic process on R that arises as a universal scaling limit in the Kardar-Parisi-Zhang (KPZ) universality class. We…

### Time-time covariance for last passage percolation in half-space

- Mathematics
- 2022

This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance,…

### Shift invariance of half space integrable models

- Mathematics
- 2022

. We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six…

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