TASEP and generalizations: Method for exact solution

Abstract

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

57 pages, revised version

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Cited by in corpus (5)

• Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy--Widom GOE distribution
• Non-intersecting path constructions for TASEP with inhomogeneous rates and the KPZ fixed point
• Exact solution of interacting particle systems related to random matrices
• On the duality between particles and polymers
• Free fermionic probability theory and K-theoretic Schubert calculus