Asymmetric Simple Exclusion Process with open boundaries and Quadratic Harnesses

Wlodek Bryc, Jacek Wesolowski

Published 2015-11-03Version 1

We establish a correspondence between a family of Markov processes called quadratic harnesses and a family of finite state asymmetric exclusion processes with open boundaries. As applications, we give a quick proof of the large deviations principle for the total number of particles in the system, and show how explicit formulas for the average occupancy of a site arise for special choices of parameters.