We analyze the one-dimensional periodic Kardar–Parisi–Zhang equation in the language of
paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer …

This note is an expanded version of a lecture I gave in fall 2021 at the MSRI program
“Universality and Integrability in Random Matrices and Interacting Particle Systems”. I will …

The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …

We provide the first construction of stationary measures for the open KPZ equation on the
spatial interval 0, 1 with general inhomogeneous Neumann boundary conditions at 0 and 1 …

We prove the existence of random dynamical systems and random attractors for a large
class of locally monotone stochastic partial differential equations perturbed by additive Lévy …

The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and
space‐continuous polymer model of a random walk in a random potential. These results …

We study the directed last-passage percolation model on the planar square lattice with
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …

We consider planar directed last-passage percolation on the square lattice with general iid
weights and study the geometry of the full set of semi-infinite geodesics in a typical …

We study the directed last-passage percolation model on the planar integer lattice with
nearest-neighbor steps and general iid weights on the vertices, outside the class of exactly …

We consider invariant measures for the stochastic Burgers equation on RR, forced by the
derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in …