A generalized asymmetric exclusion process with Uq(sl2) stochastic duality

• 成果类型: Article
• 署名作者: Carinci, Gioia; Giardina, Cristian; Redig, Frank; Sasamoto, Tomohiro
• 署名单位: Universita di Modena e Reggio Emilia; Delft University of Technology; Institute of Science Tokyo; Tokyo Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0674-0
• 发表日期: 2016
• 页码: 887-933
• 关键词: interacting particle-systems; symmetries

摘要

We study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by and where at most particles per site are allowed. The process is constructed from a -dimensional representation of a quantum Hamiltonian with invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP(q, j), we prove self-duality with several self-duality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the first q-exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from a homogeneous product measure.