TASEP and generalizations: method for exact solution

The explicit biorthogonalization method, developed in [arXiv:1701.00018] for continuous time TASEP, is generalized to a broad class of determinantal measures which describe the evolution several interacting particle systems KPZ universality class. method applied sequential and parallel update versions each four variants discrete TASEP (with Bernoulli geometric jumps, with block push dynamics) have transition probabilities; PushASEP; version update. In all cases, multipoint distribution functions are expressed terms Fredholm determinant an kernel involving hitting times certain random walks curve defined by initial data system. further caterpillars, extension models generalizes updates.