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Multi-time distribution in discrete polynuclear growth
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We study the multi-time distribution in a discrete polynuclear growth model or, equivalently, in directed last-passage percolation with geometric weights. A formula for the joint multi-time distribution function is derived in the discrete setting. It takes the form of a multiple contour integral of a block Fredholm determinant. The asymptotic multi-time distribution is then computed by taking the appropriate KPZ-scaling limit of this formula. This distribution is expected to be universal for models in the Kardar-Parisi-Zhang universality class.
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Cited by 2 Pith papers
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Two-time spatial decorrelation for the flat KPZ fixed point
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.
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Riemann surfaces for KPZ with periodic boundaries
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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