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math.PR2024
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…
math.PR2024
Periodic Pitman transforms and jointly invariant measures
Ivan Corwin, Yu Gu, Evan Sorensen
We construct explicit jointly invariant measures for the periodic KPZ equation (and therefore also the stochastic Burgers' and stochastic heat equations) for general slope paramete…
math.PR2024
Some recent progress on the periodic KPZ equation
Yu Gu, Tomasz Komorowski
We review recent progress on the study of the Kardar-Parisi-Zhang (KPZ) equation in a periodic setting, which describes the random growth of an interface in a cylindrical geometry.…