Abstract
A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric integrable ladder models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov processes with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.
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