654 citations · 2.1k across the 43 of their papers we have counts for
48 papers
Integration by parts and invariant measure for KPZ
Yu Gu, Jeremy Quastel
Using Stein's method and a Gaussian integration by parts, we provide a direct proof of the known fact that drifted Brownian motions are invariant measures (modulo height) for the K…
Global dynamics for the stochastic KdV equation with white noise as initial data
Tadahiro Oh, Jeremy Quastel, Philippe Sosoe
We study the stochastic Korteweg-de Vries equation (SKdV) with an additive space-time white noise forcing, posed on the one-dimensional torus. In particular, we construct global-in…
KPZ fluctuations in the planar stochastic heat equation
Jeremy Quastel, Alejandro Ramirez, Balint Virag
We use a version of the Skorokhod integral to give a simple and rigorous formulation of the Wick-ordered (stochastic) heat equation with planar white noise, representing the free e…
Polynuclear growth and the Toda lattice
Konstantin Matetski, Jeremy Quastel, Daniel Remenik
It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels…
Hydrodynamic large deviations of TASEP
Jeremy Quastel, Li-Cheng Tsai
We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric Simple Exclusion Process (TASEP). This problem was studied in Jensen (2000) and Varadhan (200…
Convergence of exclusion processes and KPZ equation to the KPZ fixed point
Jeremy Quastel, Sourav Sarkar
We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to t…