5 papers · 1 filter
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…
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…
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…
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…
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…