Department of Mathematics


  •  Wlodzimierz Bryc, University of Cincinnati
  •  Stationary measures of the Kardar-Parisi-Zhang equation and their limits
  •  01/25/2023
  •  3:00 PM - 3:50 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Konstantin Matetski (

I will overview recent results of [Corwin and Knizel, 2021] on the existence of stationary measures for the KPZ equation on an interval and [Barraquand and Le Doussal, 2022], [B.-Kuznetsov-Wang-Wesolowski, 2022] who found two different probabilistic descriptions of the stationary measures as a Markov process and as a measure with explicit Radon-Nikodym derivative with respect to the Brownian motion. The Markovian description leads to rigorous proofs of some of the limiting results claimed in [Barraquand and Le Doussal, 2022]. I shall discuss how the stationary measures of the KPZ equation on [0,L] behave at large scale as L goes to infinity which according to [Barraquand and Le Doussal, 2022] depending on the normalization, should correspond to stationary measures of a hypothetical KPZ fixed point on [0,1], to the stationary measure for the KPZ equation on the half-line, and to the stationary measure of a hypothetical KPZ fixed point on the half-line. The talk is based mostly on a joint work with Alexey Kuznetsov (ALEA 2022).



Department of Mathematics
Michigan State University
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