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March 2022 On inhomogeneous polynuclear growth
Kurt Johansson, Mustazee Rahman
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Ann. Probab. 50(2): 559-590 (March 2022). DOI: 10.1214/21-AOP1540

Abstract

This article studies the inhomogeneous geometric polynuclear growth model; the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions, focusing on the two-time distribution. Asymptotics of the two-time distribution in the KPZ-scaling limit is then considered, extending to two times several single-time distributions in the KPZ universality class.

Funding Statement

The first author is partially supported by grant KAW 2015.0270 from the Knut and Alice Wallenberg Foundation and grant 2015-04872 from the Swedish Science Research Council (VR).

Acknowledgments

We thank a referee for helpful comments, in particular, leading to a better Theorem 4.

Citation

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Kurt Johansson. Mustazee Rahman. "On inhomogeneous polynuclear growth." Ann. Probab. 50 (2) 559 - 590, March 2022. https://doi.org/10.1214/21-AOP1540

Information

Received: 1 December 2020; Revised: 1 June 2021; Published: March 2022
First available in Project Euclid: 24 March 2022

Digital Object Identifier: 10.1214/21-AOP1540

Subjects:
Primary: 60F05 , 60K35 , 82C23 , 82C24
Secondary: 05E10 , 15A15 , 30E20

Keywords: KPZ universality , Last passage percolation , polynuclear growth , two-time distribution

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 2 • March 2022
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