Inspired by the recent results on totally asymmetric simple exclusion processes a periodic lattice with short-ranged quenched hopping rates [A. Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study universal scaling properties of Kardar-Parisi-Zhang (KPZ) equation columnar disorder in general d-dimensions. We show that there are generic propagating modes system have their origin and ma...

We study the clustering properties of advected, noninteracting, passive scalar particles in a Burgers fluid with noise, a problem which maps to that of passive sliding particles moving under gravity on a surface evolving through the Kardar-Parisi-Zhang equation. Numerical simulations show that both the density-density correlation function and the single-site mass distribution scale with system ...

In this paper, we consider the KPZ equation under weak noise scaling. That is, introduce a small parameter $\sqrt{\varepsilon}$ in front of and let $\varepsilon \to 0$. We prove that one-point large deviation rate function has $\frac{3}{2}$ power law deep upper tail. Furthermore, by forcing value at point to be very large, limit shape as This confirms physics prediction Kolokolov Korshunov (200...

We provide a probabilistic description of the stationary measures for open KPZ on spatial interval [0, 1] in terms Markov process Y, which is Doob’s h transform Brownian motion killed at an exponential rate. Our work builds recent formula Corwin and Knizel expresses multipoint Laplace solution another $$\mathbb T$$ : continuous dual Hahn with variables taking role time-points process. The core ...

Abstract We obtain a simple formula for the stationary measure of height field evolving according to Kardar-Parisi-Zhang equation on interval with general Neumann-type boundary conditions and any size. This is achieved using recent results Corwin Knizel (arXiv:2103.12253) together Liouville quantum mechanics. Our allows easily determine in various limits: KPZ fixed point an i...

There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar–Parisi–Zhang (KPZ) in dimension d≥3 as smoothing parameter is switched off, but most of results did not hold full temperature regions where they should. Inspired by martingale techniques coming from directed polymers literature, we first extend law large numbers for SHE obtained Mukherjee e...