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arXiv · 1703.07180

Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles

Ivan Corwin·Evgeni Dimitrov
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Abstract

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 $T^{1/3}$. We prove the KPZ prediction of $T^{2/3}$ 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 $T^{2/3}$ and fluctuations scaled by $T^{1/3}$. The starting point for proving these results is a connection discovered recently by Borodin-Bufetov-Wheeler between the stochastic six vertex height function and the Hall-Littlewood process (a certain measure on plane partitions). Interpreting this process as a line ensemble with a Gibbsian resampling invariance, we show that the one-point tightness of the top curve can be propagated to the tightness of the entire curve.

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Ivan Corwin, Evgeni Dimitrov. 2017-07-06. Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles. https://doi.org/10.1007/s00220-018-3139-3

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