Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a
century, the anomalous nature of its high-temperature transport dynamics has only recently …

This work is dedicated to $\mathfrak {sl} _ {n+ 1} $-related integrable stochastic vertex
models; we call such models coloured. We prove several results about these models, which …

We consider the motion of a particle under a continuum random environment whose
distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we …

In this paper, we study lower tail probabilities of the height function $\mathfrak {h}(M, N) $ of
the stochastic six-vertex model. We introduce a novel combinatorial approach to …

We establish a symmetry in a variety of integrable stochastic systems: certain multi‐point
distributions of natural observables are unchanged under a shift of a subset of observation …

We study the stochastic heat equation (SHE)∂ tu= 1 2 Δ u+ β u ξ driven by a multiplicative
Lévy noise ξ with positive jumps and coupling constant β> 0, in arbitrary dimension d≥ 1 …

We prove a color-position symmetry for a class of ASEP-like interacting particle systems with
discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our …

Abstract We consider the (1+ 1)-dimensional stochastic heat equation (SHE) with
multiplicative white noise and the Cole-Hopf solution of the Kardar–Parisi–Zhang (KPZ) …

Law of iterated logarithms and fractal properties of the KPZ equation Page 1 The Annals of
Probability 2023, Vol. 51, No. 3, 930–986 https://doi.org/10.1214/22-AOP1603 © Institute of …