Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles

@article{Corwin2017TransversalFO,
  title={Transversal Fluctuations of the ASEP, Stochastic Six Vertex Model, and Hall-Littlewood Gibbsian Line Ensembles},
  author={Ivan Corwin and Evgeni Dimitrov},
  journal={Communications in Mathematical Physics},
  year={2017},
  volume={363},
  pages={435-501}
}
We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, T, it is known that the one-point height function fluctuations for these systems are of order T1/3. We prove the KPZ prediction of T2/3 scaling in space. Namely, we prove tightness (and Brownian absolute continuity of all subsequential limits) as T goes to infinity of the height function with spatial coordinate scaled by T2/3 and fluctuations scaled by T1/3. The starting point for proving… 

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