# 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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