A generalized asymmetric exclusion process with Uq(sl(2)) stochastic duality

作者：Carinci Gioia; Giardina Cristian; Redig Frank^*; Sasamoto Tomohiro

来源：Probability Theory and Related Fields, 2016, 166(3-4): 887-933.

DOI：10.1007/s00440-015-0674-0

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.

• 出版日期2016-12