Stochastic partial differential equations

TL;DR: In this paper, the authors introduce a regularity structure for describing functions and distributions via a kind of "jet" or local Taylor expansion around each point, which allows to describe the local behaviour not only of functions but also of large classes of distributions.

TL;DR: In this article, the authors present a survey of the development of the Kardar-Parisi-Zhang (KPZ) universality class and its application to a wide class of physical and probabilistic models.

TL;DR: In this paper, the mathematical setting of stationary systems modelled by elliptic partial differential equations with stochastic coefficients (random fields) is investigated and stability with respect to stability.

TL;DR: In this paper, the authors considered the solution of the stochastic heat equation @TZ D 1 @ 2 X ZZ P W with delta function initial condition Z and obtained explicit formulas for the one-dimensional marginal distributions, the crossover distributions, which interpolate between a standard Gaussian dis- tribution (small time) and the GUE Tracy-Widom distribution (large time).