Exact formulas for random growth with half-flat initial data

Janosch Ortmann, Jeremy Quastel, Daniel Remenik

Published 2014-07-31, updated 2015-01-20Version 2

We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially occupied. These complement earlier formulas of E. Lee [Lee10] but, unlike those formulas, ours are suitable in principle for asymptotics. We also explain how our formulas are related to divergent series formulas for half-flat KPZ of Le Doussal and Calabrese [LDC12], which we also recover using the methods of this paper. In the long time limit, formal asymptotics show that the fluctuations are given by the Airy$_{2\to1}$ marginals.