Translator Disclaimer
October 2020 The two-type Richardson model in the half-plane
Daniel Ahlberg, Maria Deijfen, Christopher Hoffman
Ann. Appl. Probab. 30(5): 2261-2273 (October 2020). DOI: 10.1214/19-AAP1557

Abstract

The two-type Richardson model describes the growth of two competing infection types on the two or higher dimensional integer lattice. For types that spread with the same intensity, it is known that there is a positive probability for infinite coexistence, while for types with different intensities, it is conjectured that infinite coexistence is not possible. In this paper we study the two-type Richardson model in the upper half-plane $\mathbb{Z}\times\mathbb{Z}_{+}$, and prove that coexistence of two types starting on the horizontal axis has positive probability if and only if the types have the same intensity.

Citation

Download Citation

Daniel Ahlberg. Maria Deijfen. Christopher Hoffman. "The two-type Richardson model in the half-plane." Ann. Appl. Probab. 30 (5) 2261 - 2273, October 2020. https://doi.org/10.1214/19-AAP1557

Information

Received: 1 November 2018; Revised: 1 September 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149528
Digital Object Identifier: 10.1214/19-AAP1557

Subjects:
Primary: 60K35

Rights: Copyright © 2020 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.30 • No. 5 • October 2020
Back to Top