Local behavior and hitting probabilities of the process

• 成果类型: Article
• 署名作者: Quastel, Jeremy; Remenik, Daniel
• 署名单位: University of Toronto; Universidad de Chile
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0466-8
• 发表日期: 2013
• 页码: 605-634
• 关键词: polynuclear growth; airy(2) processes; tasep; distributions; fluctuations; limit

摘要

We obtain a formula for the -dimensional distributions of the process in terms of a Fredholm determinant on , as opposed to the standard formula which involves extended kernels, on . The formula is analogous to an earlier formula of Prahofer and Spohn (J Stat Phys 108(5-6):1071-1106, 2002) for the process. Using this formula we are able to prove that the process is Holder continuous with exponent -and that it fluctuates locally like a Brownian motion. We also explain how the same methods can be used to obtain the analogous results for the process. As a consequence of these two results, we derive a formula for the continuum statistics of the process, analogous to that obtained in Corwin et al. (Commun Math Phys 2011, to appear) for the process.