PreprintCC BY 4.0arXiv
Half-space polynuclear growth: a multipoint Fredholm--Pfaffian formula
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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BibTeX
@misc{chen2026halfspace,
title = {{Half-space polynuclear growth: a multipoint Fredholm--Pfaffian formula}},
author = {Kailun Chen and Xincheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16989},
eprint = {2610.16989},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16989},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Half-space polynuclear growth: a multipoint Fredholm--Pfaffian formula
AU - Kailun Chen
AU - Xincheng Zhang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16989
UR - https://arxiv.org/abs/2610.16989
AB - 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.
ER -