Half-space polynuclear growth: a multipoint Fredholm--Pfaffian formula
Kailun Chen, Xincheng Zhang
Abstract
We derive a Fredholm-Pfaffian formula for the one-time multi-point transition probabilities of half-space polynuclear growth with any nonnegative boundary nucleation rate and general deterministic upper semi-continuous initial profiles. We prove the formula by showing that it satisfies an integral Kolmogorov equation with a unique bounded solution. We also discuss the formal 1:2:3 scaling limit of the kernel and its relation to the half-space KPZ fixed point.
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