Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes

• 成果类型: Article
• 署名作者: Borodin, Alexei; Corwin, Ivan; Ferrari, Patrik L.
• 署名单位: Massachusetts Institute of Technology (MIT); Columbia University; University of Bonn
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0809-6
• 发表日期: 2018
• 页码: 245-321
• 关键词: directed polymers; UNIVERSALITY; probability

摘要

We consider a discrete model for anisotropic (2 + 1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a space-time limit of covariances to those of the (2+ 1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. In particular, the bulk height function converges to the Gaussian free field which evolves according to this stochastic PDE.