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Multi-point distribution of TASEP

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arxiv 1907.09876 v5 pith:JEYWKDKG submitted 2019-07-23 math.PR math-phmath.MP

classification math.PRmath-phmath.MP
keywords distributioninitialtasepconditionsdiscretelimitingmodelmulti-point
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Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time multi-point distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity at the same speed for both step and flat initial conditions. These limiting distributions are expected to be universal for all the models in the Kardar-Parisi-Zhang universality class.

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Cited by 2 Pith papers

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  1. Two-time spatial decorrelation for the flat KPZ fixed point

    math.PR 2026-07 conditional novelty 6.0 of 10

    The two-time spatial covariance of the flat KPZ fixed point decays as exp(-c|x|^3), and normalized spatial averages converge to a Gaussian process with covariance equal to the space-integrated two-time correlation.

  2. Riemann surfaces for KPZ with periodic boundaries

    cond-mat.stat-mech 2019-08 conditional novelty 6.0 of 10

    Known exact finite-volume KPZ fluctuation probabilities are expressed as traces on Riemann surfaces for half-integer polylogarithms, and prior formulas by Prolhac and by Baik and Liu are proved equivalent.

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