EXACT FORMULAS FOR RANDOM GROWTH WITH HALF-FLAT INITIAL DATA

• 成果类型: Article
• 署名作者: Ortmann, Janosch; Quastel, Jeremy; Remenik, Daniel
• 署名单位: University of Toronto; Universidad de Chile; Universidad de Chile
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1099
• 发表日期: 2016
• 页码: 507-548
• 关键词: kpz equation; asep; distributions; particles; tasep

摘要

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 -> 1) marginals.