We review recent progress on the study of the Kardar–Parisi–Zhang (KPZ) equation in a
periodic setting, which describes the random growth of an interface in a cylindrical geometry …

We study stochastic differential equations with additive noise and distributional drift on
$\mathbb {T}^ d $ or $\mathbb {R}^ d $ and $ d\geqslant 2$. We work in a scaling …

For the KPZ equation on a torus with a 1+ 1 spacetime white noise, it was shown in Dunlap
et al.(Commun Pure Appl Math, 2023, https://doi. org/10.1002/cpa. 22110) and Gu and …

We prove a quantitative estimate on the homogenization length scale in terms of the
ellipticity ratio $\Lambda/\lambda $ of the coefficient field. This upper bound is applicable to …

For the non-gradient exclusion process, we prove its approximation rate of diffusion
matrix/conductivity by local functions. The proof follows the quantitative homogenization …

Abstract The Stochastic Burgers equation was introduced in [H. van Beijeren, R. Kutner and
H. Spohn, Excess noise for driven diffusive systems, PRL, 1985] as a continuous …

We study random walks in random environments generated by the two-dimensional
Gaussian free field. More specifically, we consider a rescaled lattice with a small mesh size …

We consider a drift-diffusion process with a time-independent and divergence-free random
drift that is of white-noise character. We are interested in the critical case of two space …

In this note, we connect two seemingly unrelated objects: On the one hand is a two-
dimensional drift-diffusion process $ X $ with divergence-free and time-independent drift $ b …

Energy solutions are a probabilistic theory for singular SPDEs with tractable (quasi-)
invariant measures. The prototypical example is the stochastic Burgers/KPZ equation with its …