Height Fluctuations for the Stationary KPZ Equation

@article{Borodin2014HeightFF,
  title={Height Fluctuations for the Stationary KPZ Equation},
  author={Alexei Borodin and Ivan Corwin and Patrik L. Ferrari and B{\'a}lint Vető},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2014},
  volume={18},
  pages={1-95}
}
We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X)$\mathcal {H}(0,X)=B(X)$, for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height function H(T,X)$\mathcal {H}(T,X)$ grow like T1/3 and converge to those previously encountered in the study of the stationary totally asymmetric simple exclusion process, polynuclear growth model and last passage percolation. The starting… 

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