Open Access
2024 Pushing, blocking and polynuclear growth
Will FitzGerald
Author Affiliations +
Electron. Commun. Probab. 29: 1-12 (2024). DOI: 10.1214/24-ECP580


We consider a discrete-time model for random interface growth which converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the addition of islands of height one according to a Poisson point process of nucleation events. The boundaries of these islands then spread in a stochastic manner, rather than at deterministic speed as in the Polynuclear growth model. The one-point distribution and multi-time distributions agree with point-to-line last passage percolation times in a geometric environment. An alternative interpretation for the growth model can be given through interacting particle systems experiencing pushing and blocking interactions.

Funding Statement

The author is supported as part of a Leverhulme Trust Research Project Grant RPG-2021-105.


Download Citation

Will FitzGerald. "Pushing, blocking and polynuclear growth." Electron. Commun. Probab. 29 1 - 12, 2024.


Received: 13 September 2023; Accepted: 17 February 2024; Published: 2024
First available in Project Euclid: 8 March 2024

Digital Object Identifier: 10.1214/24-ECP580

Primary: 60C05 , 60K35

Keywords: height function , Last passage percolation , polynuclear growth model

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