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February 2016 Exact formulas for random growth with half-flat initial data
Janosch Ortmann, Jeremy Quastel, Daniel Remenik
Ann. Appl. Probab. 26(1): 507-548 (February 2016). DOI: 10.1214/15-AAP1099


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 [J. Stat. Phys. 140 (2010) 635–647] 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 [J. Stat. Mech. 2012 (2012) P06001], which we also recover using the methods of this paper. These generating functions are given as a series without any apparent Fredholm determinant or Pfaffian structure. In the long time limit, formal asymptotics show that the fluctuations are given by the Airy$_{2\to1}$ marginals.


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Janosch Ortmann. Jeremy Quastel. Daniel Remenik. "Exact formulas for random growth with half-flat initial data." Ann. Appl. Probab. 26 (1) 507 - 548, February 2016.


Received: 1 October 2014; Revised: 1 January 2015; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1334.60212
MathSciNet: MR3449325
Digital Object Identifier: 10.1214/15-AAP1099

Primary: 60H15 , 60K35 , 82B23 , 82C22 , 82C23

Keywords: Asymmetric simple exclusion process , flat initial data , interacting particle systems , Kardar–Parisi–Zhang universality class

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.26 • No. 1 • February 2016
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